glinski_metabolites
tested hypotheses
- observed vivo versus in vitro degradation rates are the same, or observed vivo rates are lower than in vitro rates (due to other degradation processes, uptake kinetics?)
- first order kinetics are michaelis-menton, second order
- are in vitro indicative of in vivo
things to do
- michaelis menton first order comparison for both experiments
- non-linear goodness of fit
install and load supporting libraries
## nodename
## "stp-air.local"## [1] "R version 3.2.3 (2015-12-10)"##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select##
## 'drc' has been loaded.## Please cite R and 'drc' if used for a publication,## for references type 'citation()' and 'citation('drc')'.## Loading required package: lme4## Loading required package: Matrix## [1] "list of loaded packages: "## [1] "pbkrtest" "lme4" "Matrix" "scatterplot3d"
## [5] "ggplot2" "drc" "MASS" "xtable"
## [9] "zoo" "knitr" "dplyr" "rmarkdown"
## [13] "stats" "graphics" "grDevices" "utils"
## [17] "datasets" "methods" "base"import experimental exposure and microsomal data
Load csv files with experimental data and microsome data sets. The beolw may return false but still be OK if rstudio does not have privileges to data directory (e.g., attached drive).
## [1] "Root directory location: /Users/puruckertom/git/glinski_metabolites/"## [1] "check to see if R can access files OK: TRUE"experimental exposure data structure
Check out structure of imported data sets.
str(micro)## 'data.frame': 352 obs. of 6 variables:
## $ time : int 2 2 2 2 4 4 4 4 12 12 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 3.07 3.69 4.7 1.89 7.62 ...
## $ replicate: int 1 2 3 4 1 2 3 4 1 2 ...Set time and replicate fields as factors for later statistical inference.
microsome experiment data structure
Check out structure of imported data set for the microsome analysis.
str(microsome)## 'data.frame': 1123 obs. of 7 variables:
## $ time : int 0 0 0 15 15 15 30 30 30 60 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 1.208 1.596 1.362 0.551 1.347 ...
## $ replicate: int 1 2 3 1 2 3 1 2 3 1 ...
## $ microMexp: num 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...Set time and replicate fields as factors for later statistical inference.
## 'data.frame': 1123 obs. of 7 variables:
## $ time : int 0 0 0 15 15 15 30 30 30 60 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 1.208 1.596 1.362 0.551 1.347 ...
## $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 1 2 3 1 2 3 1 ...
## $ microMexp: num 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...analyze microsomal data
The microsomal experiment has 3-4 replicates for each pesticide. The experiment progressively increases the concentration of the substrate (microMexp) and measures the enzyme velocity. At each substrate concentration the reaction is quenched after a specific period of time (0, 15, 30, 60, 90 mins). This time series data is used to estimate a slope associated with each substrate concentration. Substrate concentration and linear velocity slopes are then fit using Michaelis-Menten kinetics to estimate reaction rates for each pesticide.
non-linear fitting
We use the dose-response model (drm) package from R for the fitting of the rate constant. We provide it the 2-parameter Michaelis-Menton function (mm2) as an argument. It uses the MM.2 function that is in the drc package and therefore is a drc object that contains a list of class drcMean, containing the mean function, the self starter function, the parameter names and other components such as derivatives and a function for calculating ED values. It is not shifted (??) so uses the fit f(x,(c,d,e)) = c + (d-c)/(1+e/x). Where x is the dose, it is a strictly increasing function so we reverse the sign of the slopes for the parents. e is the dose halfway between c and d, for the 2-parameter model c = 0.
## Michaelis-Menten
## (2 parameters)
## In 'drc': MM.2atrazine
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.712"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.712" "Concs = 0.712" "Concs = 0.712"
## [4] "Concs = 0.551435364" "Concs = 1.346911275" "Concs = 1.212444791"
## [7] "Concs = 1.13491833" "Concs = 1.082466929" "Concs = 1.113889522"
## [10] "Concs = 0.918015161" "Concs = 0.819916078" "Concs = 0.830401682"
## [13] "Concs = 0.60193292" "Concs = 0.514615471" "Concs = 0.543046503"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.976685 -0.003153
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37796 -0.22151 0.03239 0.21607 0.41752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.976685 0.103348 9.450 3.45e-07 ***
## Time[ind] -0.003153 0.002041 -1.545 0.146
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2554 on 13 degrees of freedom
## Multiple R-squared: 0.1551, Adjusted R-squared: 0.09013
## F-statistic: 2.387 on 1 and 13 DF, p-value: 0.1463
## (Intercept) Time[ind]
## 0.976685382 -0.003152627
## 2.5 % 97.5 %
## (Intercept) 0.753415733 1.199955031
## Time[ind] -0.007561078 0.001255824
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 10" "Concs = 10" "Concs = 10"
## [4] "Concs = 8.453642708" "Concs = 7.964608184" "Concs = 7.94451139"
## [7] "Concs = 7.680602046" "Concs = 7.527336918" "Concs = 7.478498249"
## [10] "Concs = 5.659397741" "Concs = 6.36413415" "Concs = 6.660240451"
## [13] "Concs = 6.34249619" "Concs = 5.477249479" "Concs = 5.670032215"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 9.3056 -0.0475
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7963 -0.3777 -0.1132 0.5429 0.6944
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.305616 0.225240 41.31 3.53e-15 ***
## Time[ind] -0.047498 0.004733 -10.04 1.73e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5487 on 13 degrees of freedom
## Multiple R-squared: 0.8857, Adjusted R-squared: 0.8769
## F-statistic: 100.7 on 1 and 13 DF, p-value: 1.726e-07
## (Intercept) Time[ind]
## 9.30561649 -0.04749819
## 2.5 % 97.5 %
## (Intercept) 8.81901420 9.79221878
## Time[ind] -0.05772265 -0.03727374
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 3.1684"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 3.1684" "Concs = 3.1684" "Concs = 3.1684"
## [4] "Concs = 3.840288882" "Concs = 3.471244145" "Concs = 4.21892194"
## [7] "Concs = 3.04149649" "Concs = 3.107056916" "Concs = 2.539792287"
## [10] "Concs = 2.350740689" "Concs = 2.184285874" "Concs = 1.868856626"
## [13] "Concs = 1.487945081" "Concs = 1.746448606" "Concs = 1.279189407"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 3.60836 -0.02305
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43996 -0.36681 -0.04111 0.19940 0.95630
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.608360 0.171081 21.091 1.94e-11 ***
## Time[ind] -0.023049 0.003378 -6.823 1.22e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4227 on 13 degrees of freedom
## Multiple R-squared: 0.7817, Adjusted R-squared: 0.7649
## F-statistic: 46.56 on 1 and 13 DF, p-value: 1.218e-05
## (Intercept) Time[ind]
## 3.60836007 -0.02304946
## 2.5 % 97.5 %
## (Intercept) 3.23876147 3.97795868
## Time[ind] -0.03034717 -0.01575175
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59" "Indices = 60"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 50" "Concs = 50" "Concs = 50"
## [4] "Concs = 30.1352595" "Concs = 28.31360828" "Concs = 26.0438183"
## [7] "Concs = 30.34766105" "Concs = 27.74701672" "Concs = 25.6412683"
## [10] "Concs = 28.51624079" "Concs = 26.35221344" "Concs = 24.78295594"
## [13] "Concs = 26.56519331" "Concs = 24.44743091" "Concs = 24.01565934"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 39.33 -0.20
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.2839 -5.8864 -0.9746 4.1802 10.6720
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.32803 2.97479 13.220 6.49e-09 ***
## Time[ind] -0.20002 0.05874 -3.405 0.00469 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.35 on 13 degrees of freedom
## Multiple R-squared: 0.4715, Adjusted R-squared: 0.4308
## F-statistic: 11.6 on 1 and 13 DF, p-value: 0.004694
## (Intercept) Time[ind]
## 39.3280334 -0.2000208
## 2.5 % 97.5 %
## (Intercept) 32.9013986 45.75466818
## Time[ind] -0.3269145 -0.07312715
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 61" "Indices = 62" "Indices = 63" "Indices = 64"
## [5] "Indices = 65" "Indices = 66" "Indices = 67" "Indices = 68"
## [9] "Indices = 69" "Indices = 70" "Indices = 71" "Indices = 72"
## [13] "Indices = 73" "Indices = 74" "Indices = 75"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 75" "Concs = 75" "Concs = 75"
## [4] "Concs = 29.59548976" "Concs = 36.16487256" "Concs = 37.40302159"
## [7] "Concs = 27.6465584" "Concs = 28.94210726" "Concs = 34.71955504"
## [10] "Concs = 31.19094038" "Concs = 35.96712185" "Concs = 33.12001232"
## [13] "Concs = 31.51869676" "Concs = 32.99095623" "Concs = 22.85692843"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 54.1995 -0.3519
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.325 -12.137 0.036 9.729 20.800
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 54.1995 5.8549 9.257 4.37e-07 ***
## Time[ind] -0.3519 0.1156 -3.044 0.0094 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.47 on 13 degrees of freedom
## Multiple R-squared: 0.4162, Adjusted R-squared: 0.3713
## F-statistic: 9.267 on 1 and 13 DF, p-value: 0.009404
## (Intercept) Time[ind]
## 54.1995284 -0.3519259
## 2.5 % 97.5 %
## (Intercept) 41.550828 66.8482288
## Time[ind] -0.601674 -0.1021778
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 76" "Indices = 77" "Indices = 78" "Indices = 79"
## [5] "Indices = 80" "Indices = 81" "Indices = 82" "Indices = 83"
## [9] "Indices = 84" "Indices = 85" "Indices = 86" "Indices = 87"
## [13] "Indices = 88" "Indices = 89" "Indices = 90"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 100" "Concs = 100" "Concs = 100"
## [4] "Concs = 73.12305661" "Concs = 62.97208244" "Concs = 58.17491784"
## [7] "Concs = 70.9357471" "Concs = 60.89975615" "Concs = 54.39425099"
## [10] "Concs = 67.30936536" "Concs = 56.7524779" "Concs = 50.73568923"
## [13] "Concs = 64.11432499" "Concs = 53.06960934" "Concs = 51.00465026"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 82.6524 -0.3697
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.9313 -10.1962 -0.6243 10.7902 17.3476
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 82.6524 5.3532 15.440 9.66e-10 ***
## Time[ind] -0.3697 0.1057 -3.498 0.00393 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.23 on 13 degrees of freedom
## Multiple R-squared: 0.4849, Adjusted R-squared: 0.4453
## F-statistic: 12.24 on 1 and 13 DF, p-value: 0.003928
## (Intercept) Time[ind]
## 82.6523916 -0.3697435
## 2.5 % 97.5 %
## (Intercept) 71.0875829 94.2172003
## Time[ind] -0.5980902 -0.1413968
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 91" "Indices = 92" "Indices = 93" "Indices = 94"
## [5] "Indices = 95" "Indices = 96" "Indices = 97" "Indices = 98"
## [9] "Indices = 99" "Indices = 100" "Indices = 101" "Indices = 102"
## [13] "Indices = 103" "Indices = 104"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 125" "Concs = 125" "Concs = 107.9737675"
## [4] "Concs = 85.24148342" "Concs = 85.54901737" "Concs = 158.6507932"
## [7] "Concs = 83.6386001" "Concs = 83.07467838" "Concs = 170.65218"
## [10] "Concs = 78.21161933" "Concs = 84.54185693" "Concs = 80.88478508"
## [13] "Concs = 79.00424811" "Concs = 78.20108166"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 114.3266 -0.2991
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.599 -20.830 -8.809 7.538 74.269
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 114.3266 13.6528 8.374 2.35e-06 ***
## Time[ind] -0.2991 0.2604 -1.148 0.273
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 30.85 on 12 degrees of freedom
## Multiple R-squared: 0.099, Adjusted R-squared: 0.02392
## F-statistic: 1.319 on 1 and 12 DF, p-value: 0.2732
## (Intercept) Time[ind]
## 114.3266319 -0.2990577
## 2.5 % 97.5 %
## (Intercept) 84.5797002 144.0735637
## Time[ind] -0.8664937 0.2683783
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 105" "Indices = 106" "Indices = 107" "Indices = 108"
## [5] "Indices = 109" "Indices = 110" "Indices = 111" "Indices = 112"
## [9] "Indices = 113" "Indices = 114" "Indices = 115" "Indices = 116"
## [13] "Indices = 117" "Indices = 118" "Indices = 119" "Indices = 120"
## [17] "Indices = 121" "Indices = 122" "Indices = 123" "Indices = 124"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 0" "Times = 15"
## [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 60" "Times = 90" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 150" "Concs = 150" "Concs = 150"
## [4] "Concs = 150" "Concs = 110.8050341" "Concs = 114.7205562"
## [7] "Concs = 107.1291095" "Concs = 110.2111065" "Concs = 106.4113993"
## [10] "Concs = 109.2588435" "Concs = 108.8110859" "Concs = 98.45121644"
## [13] "Concs = 105.7397626" "Concs = 103.5578664" "Concs = 109.569591"
## [16] "Concs = 103.2077499" "Concs = 96.26533592" "Concs = 104.9741825"
## [19] "Concs = 105.7942757" "Concs = 95.31462118"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 130.2975 -0.4048
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.703 -10.065 -1.362 11.312 19.703
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 130.29755 4.74893 27.437 3.87e-16 ***
## Time[ind] -0.40478 0.09377 -4.317 0.000415 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.55 on 18 degrees of freedom
## Multiple R-squared: 0.5087, Adjusted R-squared: 0.4814
## F-statistic: 18.64 on 1 and 18 DF, p-value: 0.0004153
## (Intercept) Time[ind]
## 130.2975485 -0.4047811
## 2.5 % 97.5 %
## (Intercept) 120.3204116 140.2746854
## Time[ind] -0.6017793 -0.2077829
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 125" "Indices = 126" "Indices = 127" "Indices = 128"
## [5] "Indices = 129" "Indices = 130" "Indices = 131" "Indices = 132"
## [9] "Indices = 133" "Indices = 134" "Indices = 135" "Indices = 136"
## [13] "Indices = 137" "Indices = 138" "Indices = 139"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 200" "Concs = 200" "Concs = 200"
## [4] "Concs = 200.8987987" "Concs = 134.815613" "Concs = 211.5785603"
## [7] "Concs = 193.1222732" "Concs = 210.4725656" "Concs = 213.5140511"
## [10] "Concs = 197.4425651" "Concs = 146.8087435" "Concs = 201.9011064"
## [13] "Concs = 127.9031459" "Concs = 203.6292232" "Concs = 128.0068329"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 202.5624 -0.4587
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -60.866 -15.397 4.321 22.037 42.350
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 202.5624 11.8464 17.099 2.72e-10 ***
## Time[ind] -0.4587 0.2339 -1.961 0.0717 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.27 on 13 degrees of freedom
## Multiple R-squared: 0.2283, Adjusted R-squared: 0.1689
## F-statistic: 3.846 on 1 and 13 DF, p-value: 0.07165
## (Intercept) Time[ind]
## 202.5623712 -0.4587044
## 2.5 % 97.5 %
## (Intercept) 176.9698580 228.15488441
## Time[ind] -0.9640276 0.04661879
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 140" "Indices = 141" "Indices = 142" "Indices = 143"
## [5] "Indices = 144" "Indices = 145" "Indices = 146" "Indices = 147"
## [9] "Indices = 148" "Indices = 149" "Indices = 150" "Indices = 151"
## [13] "Indices = 152" "Indices = 153" "Indices = 154"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 31" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 250" "Concs = 250" "Concs = 250"
## [4] "Concs = 111.0650322" "Concs = 110.394181" "Concs = 107.7699691"
## [7] "Concs = 110.0390245" "Concs = 133.1636589" "Concs = 106.6453068"
## [10] "Concs = 125.4094086" "Concs = 132.3152295" "Concs = 129.5529012"
## [13] "Concs = 107.9475473" "Concs = 109.2892497" "Concs = 110.9269157"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 181.5297 -0.9871
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.954 -43.575 7.248 17.415 68.470
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 181.5297 19.1185 9.495 3.27e-07 ***
## Time[ind] -0.9871 0.3772 -2.617 0.0213 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 47.18 on 13 degrees of freedom
## Multiple R-squared: 0.345, Adjusted R-squared: 0.2946
## F-statistic: 6.848 on 1 and 13 DF, p-value: 0.02131
## (Intercept) Time[ind]
## 181.5296510 -0.9870757
## 2.5 % 97.5 %
## (Intercept) 140.226690 222.832612
## Time[ind] -1.801955 -0.172196
## [1] "##################################################"## 'data.frame': 10 obs. of 2 variables:
## $ sub: num 0.712 10 3.168 50 75 ...
## $ vel: num 15.8 237.5 115.2 1000.1 1759.6 ...## sub vel
## 1 0.7120 15.76313
## 2 10.0000 237.49097
## 3 3.1684 115.24730
## 4 50.0000 1000.10406
## 5 75.0000 1759.62962
## 6 100.0000 1848.71748
## 7 125.0000 1495.28834
## 8 150.0000 2023.90534
## 9 200.0000 2293.52213
## 10 250.0000 4935.37833
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 6.6278e+04 1.2347e+05 5.3680e-01 0.6060
## e:(Intercept) 3.9443e+03 7.6952e+03 5.1257e-01 0.6221
##
## Residual standard error:
##
## 570.0903 (8 degrees of freedom)
We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.
We are fitting the 2-parameter model.
Used to estimate slopes.
dea
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.105334715" "Concs = 0.177716074" "Concs = 0.215668236"
## [7] "Concs = 0.273065521" "Concs = 0.362248011" "Concs = 0.403265809"
## [10] "Concs = 0.502168642" "Concs = 0.64289193" "Concs = 0.720570734"
## [13] "Concs = 0.725802164" "Concs = 0.865500124" "Concs = 0.956691847"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.028620 0.009439
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.15230 -0.03367 -0.01260 0.04921 0.12563
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0286203 0.0312329 0.916 0.376
## Time[ind] 0.0094387 0.0006167 15.305 1.08e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07717 on 13 degrees of freedom
## Multiple R-squared: 0.9474, Adjusted R-squared: 0.9434
## F-statistic: 234.3 on 1 and 13 DF, p-value: 1.076e-09
## (Intercept) Time[ind]
## 0.028620334 0.009438665
## 2.5 % 97.5 %
## (Intercept) -0.038854153 0.09609482
## Time[ind] 0.008106383 0.01077095
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.062527948" "Concs = 0.066722432" "Concs = 0.073739184"
## [7] "Concs = 0.13417786" "Concs = 0.142144514" "Concs = 0.153899766"
## [10] "Concs = 0.359398841" "Concs = 0.284549411" "Concs = 0.293488967"
## [13] "Concs = 0.291970799" "Concs = 0.378114427" "Concs = 0.405964967"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.004784 0.004640
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.044227 -0.008723 -0.004784 0.005104 0.076243
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.004784 0.010614 0.451 0.66
## Time[ind] 0.004640 0.000223 20.804 2.31e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02585 on 13 degrees of freedom
## Multiple R-squared: 0.9708, Adjusted R-squared: 0.9686
## F-statistic: 432.8 on 1 and 13 DF, p-value: 2.309e-11
## (Intercept) Time[ind]
## 0.004784043 0.004639529
## 2.5 % 97.5 %
## (Intercept) -0.018145174 0.027713259
## Time[ind] 0.004157742 0.005121316
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.692469949" "Concs = 0.598237597" "Concs = 0.603481745"
## [7] "Concs = 1.23886552" "Concs = 1.156190328" "Concs = 1.011651128"
## [10] "Concs = 2.056702931" "Concs = 1.850305243" "Concs = 1.516060546"
## [13] "Concs = 2.637550555" "Concs = 2.271829323" "Concs = 2.15464298"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.19461 0.02542
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.32748 -0.19461 0.02762 0.14305 0.33708
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.194607 0.086818 2.242 0.0431 *
## Time[ind] 0.025417 0.001714 14.827 1.59e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2145 on 13 degrees of freedom
## Multiple R-squared: 0.9442, Adjusted R-squared: 0.9399
## F-statistic: 219.8 on 1 and 13 DF, p-value: 1.593e-09
## (Intercept) Time[ind]
## 0.1946066 0.0254169
## 2.5 % 97.5 %
## (Intercept) 0.007046883 0.38216639
## Time[ind] 0.021713543 0.02912026
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59" "Indices = 60"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.126910879" "Concs = 0.194298986" "Concs = 0.205689666"
## [7] "Concs = 0.343048244" "Concs = 0.344665429" "Concs = 0.433300567"
## [10] "Concs = 0.79823473" "Concs = 0.910129645" "Concs = 0.789753599"
## [13] "Concs = 1.097803094" "Concs = 1.250836941" "Concs = 0.891346428"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.006856 0.012450
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.235999 -0.032614 -0.006856 0.040146 0.156281
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0068560 0.0371784 0.184 0.857
## Time[ind] 0.0124499 0.0007341 16.960 3.01e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09186 on 13 degrees of freedom
## Multiple R-squared: 0.9568, Adjusted R-squared: 0.9534
## F-statistic: 287.6 on 1 and 13 DF, p-value: 3.008e-10
## (Intercept) Time[ind]
## 0.00685602 0.01244988
## 2.5 % 97.5 %
## (Intercept) -0.07346298 0.08717502
## Time[ind] 0.01086398 0.01403577
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 61" "Indices = 62" "Indices = 63" "Indices = 64"
## [5] "Indices = 65" "Indices = 66" "Indices = 67" "Indices = 68"
## [9] "Indices = 69" "Indices = 70" "Indices = 71" "Indices = 72"
## [13] "Indices = 73"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.660583406" "Concs = 0.521827731" "Concs = 0.519014334"
## [7] "Concs = 0.937060708" "Concs = 0.947234926" "Concs = 1.586433592"
## [10] "Concs = 1.701961252" "Concs = 2.098184546" "Concs = 2.114078113"
## [13] "Concs = 1.9947066"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.15067 0.02247
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.1782 -0.1507 0.0313 0.1123 0.2031
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.150670 0.058446 2.578 0.0257 *
## Time[ind] 0.022469 0.001143 19.654 6.44e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1406 on 11 degrees of freedom
## Multiple R-squared: 0.9723, Adjusted R-squared: 0.9698
## F-statistic: 386.3 on 1 and 11 DF, p-value: 6.445e-10
## (Intercept) Time[ind]
## 0.15066966 0.02246945
## 2.5 % 97.5 %
## (Intercept) 0.02203109 0.27930823
## Time[ind] 0.01995315 0.02498576
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 0.712"
## [1] "Indices = 74" "Indices = 75" "Indices = 76" "Indices = 77"
## [5] "Indices = 78" "Indices = 79" "Indices = 80" "Indices = 81"
## [9] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [13] "Indices = 86" "Indices = 87"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0 0
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## 0 0 0 0 0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0 0 NA NA
## Time[ind] 0 0 NA NA
##
## Residual standard error: 0 on 12 degrees of freedom
## Multiple R-squared: NaN, Adjusted R-squared: NaN
## F-statistic: NaN on 1 and 12 DF, p-value: NA
## (Intercept) Time[ind]
## 0 0
## 2.5 % 97.5 %
## (Intercept) 0 0
## Time[ind] 0 0
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 3.1684"
## [1] "Indices = 88" "Indices = 89" "Indices = 90" "Indices = 91"
## [5] "Indices = 92" "Indices = 93" "Indices = 94" "Indices = 95"
## [9] "Indices = 96" "Indices = 97" "Indices = 98" "Indices = 99"
## [13] "Indices = 100" "Indices = 101" "Indices = 102"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0" "Concs = 0"
## [7] "Concs = 0" "Concs = 0" "Concs = 0"
## [10] "Concs = 0.004276181" "Concs = 0" "Concs = 0"
## [13] "Concs = 0.068958259" "Concs = 0.095246481" "Concs = 0.042564751"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## -0.0124160 0.0006791
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.028331 -0.007958 0.002229 0.012416 0.046542
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0124160 0.0082982 -1.496 0.15847
## Time[ind] 0.0006791 0.0001638 4.145 0.00115 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0205 on 13 degrees of freedom
## Multiple R-squared: 0.5692, Adjusted R-squared: 0.5361
## F-statistic: 17.18 on 1 and 13 DF, p-value: 0.001152
## (Intercept) Time[ind]
## -0.0124160299 0.0006791216
## 2.5 % 97.5 %
## (Intercept) -0.0303432318 0.005511172
## Time[ind] 0.0003251496 0.001033094
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 103" "Indices = 104" "Indices = 105" "Indices = 106"
## [5] "Indices = 107" "Indices = 108" "Indices = 109" "Indices = 110"
## [9] "Indices = 111" "Indices = 112" "Indices = 113" "Indices = 114"
## [13] "Indices = 115" "Indices = 116" "Indices = 117"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0" "Concs = 0"
## [7] "Concs = 0" "Concs = 0" "Concs = 0"
## [10] "Concs = 0" "Concs = 0.08814803" "Concs = 0"
## [13] "Concs = 0.636612173" "Concs = 0.308057976" "Concs = 0.343301822"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## -0.076456 0.004313
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.18231 -0.05293 0.01176 0.05403 0.32492
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.076456 0.051227 -1.492 0.159438
## Time[ind] 0.004313 0.001011 4.264 0.000923 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1266 on 13 degrees of freedom
## Multiple R-squared: 0.5831, Adjusted R-squared: 0.551
## F-statistic: 18.18 on 1 and 13 DF, p-value: 0.0009232
## (Intercept) Time[ind]
## -0.076455952 0.004312751
## 2.5 % 97.5 %
## (Intercept) -0.187125601 0.034213697
## Time[ind] 0.002127583 0.006497919
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 118" "Indices = 119" "Indices = 120" "Indices = 121"
## [5] "Indices = 122" "Indices = 123" "Indices = 124" "Indices = 125"
## [9] "Indices = 126" "Indices = 127" "Indices = 128" "Indices = 129"
## [13] "Indices = 130"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.303186347" "Concs = 0.314346484" "Concs = 0.32890249"
## [7] "Concs = 0.470955087" "Concs = 0.418661875" "Concs = 0.69686814"
## [10] "Concs = 0.65732937" "Concs = 1.058297138" "Concs = 1.054151944"
## [13] "Concs = 0.826804017"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.08568 0.01013
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.17082 -0.08568 0.02900 0.06552 0.09123
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0856770 0.0366138 2.34 0.0392 *
## Time[ind] 0.0101327 0.0007162 14.15 2.11e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08809 on 11 degrees of freedom
## Multiple R-squared: 0.9479, Adjusted R-squared: 0.9432
## F-statistic: 200.2 on 1 and 11 DF, p-value: 2.106e-08
## (Intercept) Time[ind]
## 0.08567696 0.01013273
## 2.5 % 97.5 %
## (Intercept) 0.005090447 0.16626348
## Time[ind] 0.008556376 0.01170909
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 131" "Indices = 132" "Indices = 133" "Indices = 134"
## [5] "Indices = 135" "Indices = 136" "Indices = 137" "Indices = 138"
## [9] "Indices = 139" "Indices = 140" "Indices = 141" "Indices = 142"
## [13] "Indices = 143" "Indices = 144" "Indices = 145" "Indices = 146"
## [17] "Indices = 147" "Indices = 148"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 0" "Times = 15"
## [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0.651134538" "Concs = 0.410418033"
## [7] "Concs = 0.72633168" "Concs = 0.655344167" "Concs = 1.213331632"
## [10] "Concs = 0.938854783" "Concs = 1.336588359" "Concs = 1.220393789"
## [13] "Concs = 2.258618197" "Concs = 2.185187246" "Concs = 2.037689206"
## [16] "Concs = 2.794152863" "Concs = 2.97663412" "Concs = 2.702787847"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.12001 0.03166
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.26683 -0.12001 0.01248 0.14043 0.26671
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.120012 0.058315 2.058 0.0563 .
## Time[ind] 0.031662 0.001243 25.467 2.24e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1647 on 16 degrees of freedom
## Multiple R-squared: 0.9759, Adjusted R-squared: 0.9744
## F-statistic: 648.6 on 1 and 16 DF, p-value: 2.241e-14
## (Intercept) Time[ind]
## 0.12001167 0.03166231
## 2.5 % 97.5 %
## (Intercept) -0.003610993 0.24363433
## Time[ind] 0.029026668 0.03429796
## [1] "##################################################"## 'data.frame': 10 obs. of 2 variables:
## $ sub: num 50 10 100 75 125 ...
## $ vel: num 47.2 23.2 127.1 62.2 112.3 ...## sub vel
## 1 50.0000 47.193323
## 2 10.0000 23.197644
## 3 100.0000 127.084516
## 4 75.0000 62.249384
## 5 125.0000 112.347269
## 6 0.7120 0.000000
## 7 3.1684 3.395608
## 8 200.0000 21.563755
## 9 250.0000 50.663660
## 10 150.0000 158.311559
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 98.19750 30.06129 3.26658 0.0114
## e:(Intercept) 21.80965 30.56362 0.71358 0.4958
##
## Residual standard error:
##
## 43.44814 (8 degrees of freedom)
We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.
We are fitting the 2-parameter model.
Used to estimate slopes.
dia
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.17588934" "Concs = 0.162027282" "Concs = 0.163356559"
## [7] "Concs = 0.343213005" "Concs = 0.307927387" "Concs = 0.309459105"
## [10] "Concs = 0.560097677" "Concs = 0.54821645" "Concs = 0.533109282"
## [13] "Concs = 0.73827321" "Concs = 0.728694143" "Concs = 0.726811372"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.040150 0.008025
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.040150 -0.034677 0.002826 0.026782 0.062303
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0401505 0.0141144 2.845 0.0138 *
## Time[ind] 0.0080253 0.0002787 28.797 3.67e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03488 on 13 degrees of freedom
## Multiple R-squared: 0.9846, Adjusted R-squared: 0.9834
## F-statistic: 829.3 on 1 and 13 DF, p-value: 3.671e-13
## (Intercept) Time[ind]
## 0.040150483 0.008025329
## 2.5 % 97.5 %
## (Intercept) 0.009658192 0.070642775
## Time[ind] 0.007423260 0.008627398
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.037225886" "Concs = 0.038369499" "Concs = 0.046312162"
## [7] "Concs = 0.08490015" "Concs = 0.083838648" "Concs = 0.093345378"
## [10] "Concs = 0.209721193" "Concs = 0.168743119" "Concs = 0.161851994"
## [13] "Concs = 0.162150446" "Concs = 0.222852555" "Concs = 0.229604672"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.004532 0.002650
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.020209 -0.005225 -0.001700 0.001442 0.046169
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0045322 0.0062267 0.728 0.48
## Time[ind] 0.0026503 0.0001308 20.257 3.23e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01517 on 13 degrees of freedom
## Multiple R-squared: 0.9693, Adjusted R-squared: 0.9669
## F-statistic: 410.3 on 1 and 13 DF, p-value: 3.233e-11
## (Intercept) Time[ind]
## 0.004532231 0.002650328
## 2.5 % 97.5 %
## (Intercept) -0.008919788 0.017984250
## Time[ind] 0.002367676 0.002932981
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.519984026" "Concs = 0.456185794" "Concs = 0.465640368"
## [7] "Concs = 0.969762496" "Concs = 0.925948373" "Concs = 0.828633383"
## [10] "Concs = 1.646101156" "Concs = 1.493978674" "Concs = 1.273473826"
## [13] "Concs = 2.097846916" "Concs = 1.845660879" "Concs = 1.775884862"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.14326 0.02077
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.23664 -0.14326 0.01084 0.09494 0.25667
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.14326 0.06330 2.263 0.0414 *
## Time[ind] 0.02077 0.00125 16.617 3.88e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1564 on 13 degrees of freedom
## Multiple R-squared: 0.955, Adjusted R-squared: 0.9516
## F-statistic: 276.1 on 1 and 13 DF, p-value: 3.88e-10
## (Intercept) Time[ind]
## 0.14326104 0.02076955
## 2.5 % 97.5 %
## (Intercept) 0.006505081 0.28001700
## Time[ind] 0.018069306 0.02346979
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59" "Indices = 60"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.105167732" "Concs = 0.164272494" "Concs = 0.177858813"
## [7] "Concs = 0.289730134" "Concs = 0.302066953" "Concs = 0.387892352"
## [10] "Concs = 0.703975509" "Concs = 0.8027739" "Concs = 0.718751156"
## [13] "Concs = 0.974859321" "Concs = 1.104369407" "Concs = 0.769135715"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.003918 0.011012
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.225872 -0.026182 -0.003918 0.046471 0.138129
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0039178 0.0349716 0.112 0.913
## Time[ind] 0.0110121 0.0006905 15.948 6.47e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08641 on 13 degrees of freedom
## Multiple R-squared: 0.9514, Adjusted R-squared: 0.9476
## F-statistic: 254.3 on 1 and 13 DF, p-value: 6.468e-10
## (Intercept) Time[ind]
## 0.003917758 0.011012115
## 2.5 % 97.5 %
## (Intercept) -0.071633704 0.07946922
## Time[ind] 0.009520354 0.01250388
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 61" "Indices = 62" "Indices = 63" "Indices = 64"
## [5] "Indices = 65" "Indices = 66" "Indices = 67" "Indices = 68"
## [9] "Indices = 69" "Indices = 70" "Indices = 71" "Indices = 72"
## [13] "Indices = 73"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.558156141" "Concs = 0.453398653" "Concs = 0.457441572"
## [7] "Concs = 0.819739976" "Concs = 0.818340148" "Concs = 1.39707951"
## [10] "Concs = 1.483198815" "Concs = 1.818559552" "Concs = 1.850457042"
## [13] "Concs = 1.741234977"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.12932 0.01963
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.15472 -0.12932 0.02964 0.10015 0.17613
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.1293156 0.0503960 2.566 0.0262 *
## Time[ind] 0.0196293 0.0009858 19.912 5.6e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1212 on 11 degrees of freedom
## Multiple R-squared: 0.973, Adjusted R-squared: 0.9706
## F-statistic: 396.5 on 1 and 11 DF, p-value: 5.603e-10
## (Intercept) Time[ind]
## 0.1293156 0.0196293
## 2.5 % 97.5 %
## (Intercept) 0.01839473 0.24023649
## Time[ind] 0.01745957 0.02179903
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 0.712"
## [1] "Indices = 74" "Indices = 75" "Indices = 76" "Indices = 77"
## [5] "Indices = 78" "Indices = 79" "Indices = 80" "Indices = 81"
## [9] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [13] "Indices = 86" "Indices = 87" "Indices = 88"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0 0
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## 0 0 0 0 0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0 0 NA NA
## Time[ind] 0 0 NA NA
##
## Residual standard error: 0 on 13 degrees of freedom
## Multiple R-squared: NaN, Adjusted R-squared: NaN
## F-statistic: NaN on 1 and 13 DF, p-value: NA
## (Intercept) Time[ind]
## 0 0
## 2.5 % 97.5 %
## (Intercept) 0 0
## Time[ind] 0 0
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 3.1684"
## [1] "Indices = 89" "Indices = 90" "Indices = 91" "Indices = 92"
## [5] "Indices = 93" "Indices = 94" "Indices = 95" "Indices = 96"
## [9] "Indices = 97" "Indices = 98" "Indices = 99" "Indices = 100"
## [13] "Indices = 101" "Indices = 102" "Indices = 103"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0 0
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## 0 0 0 0 0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0 0 NA NA
## Time[ind] 0 0 NA NA
##
## Residual standard error: 0 on 13 degrees of freedom
## Multiple R-squared: NaN, Adjusted R-squared: NaN
## F-statistic: NaN on 1 and 13 DF, p-value: NA
## (Intercept) Time[ind]
## 0 0
## 2.5 % 97.5 %
## (Intercept) 0 0
## Time[ind] 0 0
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 104" "Indices = 105" "Indices = 106" "Indices = 107"
## [5] "Indices = 108" "Indices = 109" "Indices = 110" "Indices = 111"
## [9] "Indices = 112" "Indices = 113" "Indices = 114" "Indices = 115"
## [13] "Indices = 116"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.488073154" "Concs = 0.494203709" "Concs = 0.58569046"
## [7] "Concs = 0.731173258" "Concs = 0.714667917" "Concs = 1.145221545"
## [10] "Concs = 1.154181588" "Concs = 1.638731263" "Concs = 1.563749853"
## [13] "Concs = 1.475092589"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.15075 0.01622
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.15075 -0.13584 0.02780 0.09369 0.19157
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.1507544 0.0503259 2.996 0.0122 *
## Time[ind] 0.0162242 0.0009844 16.481 4.21e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1211 on 11 degrees of freedom
## Multiple R-squared: 0.9611, Adjusted R-squared: 0.9575
## F-statistic: 271.6 on 1 and 11 DF, p-value: 4.214e-09
## (Intercept) Time[ind]
## 0.1507544 0.0162242
## 2.5 % 97.5 %
## (Intercept) 0.03998791 0.26152088
## Time[ind] 0.01405749 0.01839091
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 117" "Indices = 118" "Indices = 119" "Indices = 120"
## [5] "Indices = 121" "Indices = 122" "Indices = 123" "Indices = 124"
## [9] "Indices = 125" "Indices = 126" "Indices = 127" "Indices = 128"
## [13] "Indices = 129" "Indices = 130" "Indices = 131" "Indices = 132"
## [17] "Indices = 133" "Indices = 134"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 0" "Times = 15"
## [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0.462309631" "Concs = 0.255700106"
## [7] "Concs = 0.526463046" "Concs = 0.47230486" "Concs = 0.931548447"
## [10] "Concs = 0.722337549" "Concs = 1.066740758" "Concs = 0.948249061"
## [13] "Concs = 1.827879364" "Concs = 1.789768545" "Concs = 1.614786398"
## [16] "Concs = 2.243971727" "Concs = 2.385364241" "Concs = 2.16439478"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.06633 0.02574
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.21878 -0.06632 0.00304 0.08820 0.22813
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.066325 0.048063 1.38 0.187
## Time[ind] 0.025743 0.001025 25.12 2.77e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1357 on 16 degrees of freedom
## Multiple R-squared: 0.9753, Adjusted R-squared: 0.9737
## F-statistic: 631.1 on 1 and 16 DF, p-value: 2.773e-14
## (Intercept) Time[ind]
## 0.0663253 0.0257428
## 2.5 % 97.5 %
## (Intercept) -0.03556328 0.16821388
## Time[ind] 0.02357053 0.02791507
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 135" "Indices = 136" "Indices = 137" "Indices = 138"
## [5] "Indices = 139" "Indices = 140" "Indices = 141" "Indices = 142"
## [9] "Indices = 143" "Indices = 144" "Indices = 145" "Indices = 146"
## [13] "Indices = 147" "Indices = 148" "Indices = 149"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0" "Concs = 0"
## [7] "Concs = 0" "Concs = 0" "Concs = 0"
## [10] "Concs = 0.147179292" "Concs = 0.49374336" "Concs = 0.185151589"
## [13] "Concs = 0.905020781" "Concs = 0.751527127" "Concs = 0.778803003"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## -0.135092 0.009039
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.260068 -0.136078 -0.000493 0.117739 0.226604
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.135092 0.061636 -2.192 0.0472 *
## Time[ind] 0.009039 0.001217 7.427 4.99e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1523 on 13 degrees of freedom
## Multiple R-squared: 0.8093, Adjusted R-squared: 0.7946
## F-statistic: 55.16 on 1 and 13 DF, p-value: 4.994e-06
## (Intercept) Time[ind]
## -0.135091948 0.009038982
## 2.5 % 97.5 %
## (Intercept) -0.268247657 -0.001936239
## Time[ind] 0.006409827 0.011668136
## [1] "##################################################"## 'data.frame': 10 obs. of 2 variables:
## $ sub: num 50 10 100 75 125 ...
## $ vel: num 40.1 13.3 103.8 55.1 98.1 ...## sub vel
## 1 50.0000 40.12665
## 2 10.0000 13.25164
## 3 100.0000 103.84774
## 4 75.0000 55.06057
## 5 125.0000 98.14650
## 6 0.7120 0.00000
## 7 3.1684 0.00000
## 8 250.0000 81.12099
## 9 150.0000 128.71399
## 10 200.0000 45.19491
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 110.2228 30.3572 3.6309 0.0067
## e:(Intercept) 45.5107 42.1869 1.0788 0.3121
##
## Residual standard error:
##
## 26.84532 (8 degrees of freedom)
triadimefon
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.68082"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.68082" "Concs = 0.68082" "Concs = 0.68082"
## [4] "Concs = 0.399443695" "Concs = 0.42224169" "Concs = 0.36799564"
## [7] "Concs = 0.335043095" "Concs = 0.307545884" "Concs = 0.33049829"
## [10] "Concs = 0.298781298" "Concs = 0.300851183" "Concs = 0.297372843"
## [13] "Concs = 0.30988245" "Concs = 0.29724505" "Concs = 0.293730776"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.530169 -0.003332
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.12265 -0.08795 -0.03145 0.07331 0.15065
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.5301692 0.0423540 12.518 1.26e-08 ***
## Time[ind] -0.0033324 0.0008363 -3.985 0.00156 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1047 on 13 degrees of freedom
## Multiple R-squared: 0.5498, Adjusted R-squared: 0.5152
## F-statistic: 15.88 on 1 and 13 DF, p-value: 0.001556
## (Intercept) Time[ind]
## 0.530169234 -0.003332387
## 2.5 % 97.5 %
## (Intercept) 0.438669087 0.62166938
## Time[ind] -0.005139054 -0.00152572
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 10" "Concs = 10" "Concs = 10"
## [4] "Concs = 3.796829723" "Concs = 3.995422538" "Concs = 4.084402023"
## [7] "Concs = 3.689670522" "Concs = 3.770627455" "Concs = 3.708045842"
## [10] "Concs = 2.923805377" "Concs = 2.81999575" "Concs = 1.627429272"
## [13] "Concs = 1.556106647" "Concs = 1.615639352"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 7.24520 -0.07209
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.36709 -1.38837 -0.04818 0.86696 2.75480
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.24520 0.78504 9.229 8.46e-07 ***
## Time[ind] -0.07209 0.01573 -4.583 0.000629 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.938 on 12 degrees of freedom
## Multiple R-squared: 0.6364, Adjusted R-squared: 0.6061
## F-statistic: 21 on 1 and 12 DF, p-value: 0.0006292
## (Intercept) Time[ind]
## 7.24519589 -0.07208527
## 2.5 % 97.5 %
## (Intercept) 5.5347334 8.95565838
## Time[ind] -0.1063558 -0.03781477
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 30" "Indices = 31" "Indices = 32" "Indices = 33"
## [5] "Indices = 34" "Indices = 35" "Indices = 36" "Indices = 37"
## [9] "Indices = 38" "Indices = 39" "Indices = 40" "Indices = 41"
## [13] "Indices = 42" "Indices = 43" "Indices = 44"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 2.89" "Concs = 2.89" "Concs = 2.89"
## [4] "Concs = 1.438977536" "Concs = 1.147878572" "Concs = 1.273836719"
## [7] "Concs = 1.170628317" "Concs = 1.153347335" "Concs = 0.90609785"
## [10] "Concs = 0.796555881" "Concs = 0.724314066" "Concs = 0.705525399"
## [13] "Concs = 0.684015583" "Concs = 0.645877009" "Concs = 0.633912406"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 2.10944 -0.01998
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6618 -0.3636 -0.1861 0.3541 0.7806
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.109439 0.217151 9.714 2.52e-07 ***
## Time[ind] -0.019984 0.004288 -4.661 0.000446 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5366 on 13 degrees of freedom
## Multiple R-squared: 0.6256, Adjusted R-squared: 0.5968
## F-statistic: 21.72 on 1 and 13 DF, p-value: 0.0004457
## (Intercept) Time[ind]
## 2.10943918 -0.01998397
## 2.5 % 97.5 %
## (Intercept) 1.64031311 2.57856525
## Time[ind] -0.02924684 -0.01072109
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 45" "Indices = 46" "Indices = 47" "Indices = 48"
## [5] "Indices = 49" "Indices = 50" "Indices = 51" "Indices = 52"
## [9] "Indices = 53" "Indices = 54" "Indices = 55" "Indices = 56"
## [13] "Indices = 57"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 50" "Concs = 50" "Concs = 50"
## [4] "Concs = 25.6223204" "Concs = 24.15898057" "Concs = 24.97516518"
## [7] "Concs = 26.62994332" "Concs = 26.25228145" "Concs = 25.95782864"
## [10] "Concs = 28.59868326" "Concs = 22.32352998" "Concs = 22.61126729"
## [13] "Concs = 22.93204565"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 38.6877 -0.2078
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.411 -6.200 2.341 2.950 11.312
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 38.68774 3.59860 10.751 3.57e-07 ***
## Time[ind] -0.20784 0.07039 -2.953 0.0131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.658 on 11 degrees of freedom
## Multiple R-squared: 0.4421, Adjusted R-squared: 0.3914
## F-statistic: 8.717 on 1 and 11 DF, p-value: 0.01315
## (Intercept) Time[ind]
## 38.6877394 -0.2078355
## 2.5 % 97.5 %
## (Intercept) 30.7672635 46.60821530
## Time[ind] -0.3627682 -0.05290274
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 58" "Indices = 59" "Indices = 60" "Indices = 61"
## [5] "Indices = 62" "Indices = 63" "Indices = 64" "Indices = 65"
## [9] "Indices = 66" "Indices = 67" "Indices = 68" "Indices = 69"
## [13] "Indices = 70" "Indices = 71" "Indices = 72"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 75" "Concs = 75" "Concs = 75"
## [4] "Concs = 39.60290919" "Concs = 36.37647057" "Concs = 38.41537648"
## [7] "Concs = 41.36228948" "Concs = 39.60347726" "Concs = 37.05197615"
## [10] "Concs = 38.79077057" "Concs = 39.14694989" "Concs = 38.88285882"
## [13] "Concs = 38.84162326" "Concs = 38.38496898" "Concs = 38.08875118"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 56.5500 -0.2713
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.104 -10.084 -1.390 6.479 18.450
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 56.55000 5.05169 11.19 4.79e-08 ***
## Time[ind] -0.27128 0.09975 -2.72 0.0175 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.48 on 13 degrees of freedom
## Multiple R-squared: 0.3627, Adjusted R-squared: 0.3136
## F-statistic: 7.397 on 1 and 13 DF, p-value: 0.01752
## (Intercept) Time[ind]
## 56.5500000 -0.2712847
## 2.5 % 97.5 %
## (Intercept) 45.6364964 67.46350349
## Time[ind] -0.4867715 -0.05579803
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 73" "Indices = 74" "Indices = 75" "Indices = 76"
## [5] "Indices = 77" "Indices = 78" "Indices = 79" "Indices = 80"
## [9] "Indices = 81" "Indices = 82" "Indices = 83" "Indices = 84"
## [13] "Indices = 85" "Indices = 86" "Indices = 87"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 100" "Concs = 100" "Concs = 100"
## [4] "Concs = 49.24893567" "Concs = 52.23999837" "Concs = 54.94800062"
## [7] "Concs = 51.63283427" "Concs = 55.62979138" "Concs = 53.25296347"
## [10] "Concs = 57.2285182" "Concs = 52.25557462" "Concs = 57.56142454"
## [13] "Concs = 55.15134637" "Concs = 52.80788424" "Concs = 54.77096052"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 75.7963 -0.3252
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.6700 -13.5987 0.9416 8.4289 24.2037
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 75.7963 6.6510 11.396 3.87e-08 ***
## Time[ind] -0.3252 0.1313 -2.476 0.0278 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.43 on 13 degrees of freedom
## Multiple R-squared: 0.3205, Adjusted R-squared: 0.2682
## F-statistic: 6.131 on 1 and 13 DF, p-value: 0.02782
## (Intercept) Time[ind]
## 75.7962700 -0.3251552
## 2.5 % 97.5 %
## (Intercept) 61.427706 90.16483448
## Time[ind] -0.608862 -0.04144848
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 88" "Indices = 89" "Indices = 90" "Indices = 91"
## [5] "Indices = 92" "Indices = 93" "Indices = 94" "Indices = 95"
## [9] "Indices = 96" "Indices = 97" "Indices = 98" "Indices = 99"
## [13] "Indices = 100" "Indices = 101"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 125" "Concs = 125" "Concs = 125"
## [4] "Concs = 54.97761564" "Concs = 64.19295623" "Concs = 61.97688614"
## [7] "Concs = 68.89112849" "Concs = 56.33566744" "Concs = 71.31751913"
## [10] "Concs = 66.04862513" "Concs = 69.71262134" "Concs = 57.48171016"
## [13] "Concs = 60.79276739" "Concs = 57.42314849"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 94.1185 -0.4829
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -31.898 -19.697 2.735 9.305 30.881
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 94.1185 9.0233 10.431 2.27e-07 ***
## Time[ind] -0.4829 0.1808 -2.671 0.0204 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.28 on 12 degrees of freedom
## Multiple R-squared: 0.3728, Adjusted R-squared: 0.3206
## F-statistic: 7.134 on 1 and 12 DF, p-value: 0.02038
## (Intercept) Time[ind]
## 94.1185302 -0.4828739
## 2.5 % 97.5 %
## (Intercept) 74.4584918 113.77856852
## Time[ind] -0.8767787 -0.08896906
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 102" "Indices = 103" "Indices = 104" "Indices = 105"
## [5] "Indices = 106" "Indices = 107" "Indices = 108" "Indices = 109"
## [9] "Indices = 110" "Indices = 111" "Indices = 112" "Indices = 113"
## [13] "Indices = 114" "Indices = 115"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 150" "Concs = 150" "Concs = 78.63355587"
## [4] "Concs = 62.93987056" "Concs = 106.7018113" "Concs = 73.37624336"
## [7] "Concs = 66.9635187" "Concs = 95.5133834" "Concs = 69.7678651"
## [10] "Concs = 58.53815945" "Concs = 61.06336245" "Concs = 82.43537943"
## [13] "Concs = 75.76324133" "Concs = 73.77914496"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 107.9411 -0.5226
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.163 -18.678 -1.785 14.357 42.059
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 107.9411 11.3512 9.509 6.15e-07 ***
## Time[ind] -0.5226 0.2165 -2.413 0.0327 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.65 on 12 degrees of freedom
## Multiple R-squared: 0.3268, Adjusted R-squared: 0.2707
## F-statistic: 5.824 on 1 and 12 DF, p-value: 0.03271
## (Intercept) Time[ind]
## 107.9411403 -0.5225648
## 2.5 % 97.5 %
## (Intercept) 83.2090866 132.67319401
## Time[ind] -0.9943398 -0.05078988
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 116" "Indices = 117" "Indices = 118" "Indices = 119"
## [5] "Indices = 120" "Indices = 121" "Indices = 122" "Indices = 123"
## [9] "Indices = 124" "Indices = 125" "Indices = 126" "Indices = 127"
## [13] "Indices = 128" "Indices = 129" "Indices = 130"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 200" "Concs = 200" "Concs = 200"
## [4] "Concs = 338.7826757" "Concs = 357.9520843" "Concs = 202.0964578"
## [7] "Concs = 422.3552358" "Concs = 340.5253492" "Concs = 345.8291382"
## [10] "Concs = 359.4674526" "Concs = 377.2730298" "Concs = 186.1093226"
## [13] "Concs = 471.6047045" "Concs = 376.1365036" "Concs = 190.6933116"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 261.28 1.11
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -170.53 -61.28 31.56 56.04 127.76
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 261.2807 37.7669 6.918 1.06e-05 ***
## Time[ind] 1.1105 0.7457 1.489 0.16
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 93.32 on 13 degrees of freedom
## Multiple R-squared: 0.1457, Adjusted R-squared: 0.08001
## F-statistic: 2.217 on 1 and 13 DF, p-value: 0.1603
## (Intercept) Time[ind]
## 261.280745 1.110451
## 2.5 % 97.5 %
## (Intercept) 179.6902783 342.871211
## Time[ind] -0.5005493 2.721452
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 131" "Indices = 132" "Indices = 133" "Indices = 134"
## [5] "Indices = 135" "Indices = 136" "Indices = 137" "Indices = 138"
## [9] "Indices = 139" "Indices = 140" "Indices = 141" "Indices = 142"
## [13] "Indices = 143" "Indices = 144"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 250" "Concs = 250" "Concs = 186.8824662"
## [4] "Concs = 208.9457498" "Concs = 167.0779465" "Concs = 229.5166359"
## [7] "Concs = 99.11335239" "Concs = 263.0350796" "Concs = 59.52448054"
## [10] "Concs = 46.29054385" "Concs = 51.98182232" "Concs = 162.0360626"
## [13] "Concs = 200.5560551" "Concs = 187.8908429"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 209.0664 -0.9642
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -104.92 -67.65 27.05 47.27 82.90
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 209.0664 31.6894 6.597 2.55e-05 ***
## Time[ind] -0.9642 0.6045 -1.595 0.137
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 71.6 on 12 degrees of freedom
## Multiple R-squared: 0.1749, Adjusted R-squared: 0.1062
## F-statistic: 2.544 on 1 and 12 DF, p-value: 0.1367
## (Intercept) Time[ind]
## 209.0664272 -0.9642375
## 2.5 % 97.5 %
## (Intercept) 140.021166 278.1116888
## Time[ind] -2.281307 0.3528317
## [1] "##################################################"## 'data.frame': 10 obs. of 2 variables:
## $ sub: num 0.681 10 2.89 50 75 ...
## $ vel: num -16.7 -360.4 -99.9 -1039.2 -1356.4 ...## sub vel
## 1 0.68082 -16.66194
## 2 10.00000 -360.42636
## 3 2.89000 -99.91984
## 4 50.00000 -1039.17744
## 5 75.00000 -1356.42374
## 6 100.00000 -1625.77622
## 7 125.00000 -2414.36930
## 8 150.00000 -2612.82417
## 9 200.00000 5552.25724
## 10 250.00000 -4821.18755
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) -1300.61498 1522.95929 -0.85401 0.4179
## e:(Intercept) 13.12748 81.35072 0.16137 0.8758
##
## Residual standard error:
##
## 2797.647 (8 degrees of freedom)
tdla
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.68"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.124349504" "Concs = 0.14627783" "Concs = 0.089752887"
## [7] "Concs = 0.107638677" "Concs = 0.159434476" "Concs = 0.159787554"
## [10] "Concs = 0.099828091" "Concs = 0.225228369" "Concs = 0.139329405"
## [13] "Concs = 0.072482112" "Concs = 0.09994686" "Concs = 0.061506341"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.076146 0.000587
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.076146 -0.061979 0.004803 0.050363 0.113865
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0761457 0.0260993 2.918 0.012 *
## Time[ind] 0.0005870 0.0005153 1.139 0.275
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06449 on 13 degrees of freedom
## Multiple R-squared: 0.09074, Adjusted R-squared: 0.0208
## F-statistic: 1.297 on 1 and 13 DF, p-value: 0.2753
## (Intercept) Time[ind]
## 0.0761456879 0.0005869689
## 2.5 % 97.5 %
## (Intercept) 0.0197616122 0.13252976
## Time[ind] -0.0005263326 0.00170027
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.562008549" "Concs = 0.514503123" "Concs = 0.553400833"
## [7] "Concs = 0.914781067" "Concs = 0.896944628" "Concs = 0.854682343"
## [10] "Concs = 0.640465968" "Concs = 1.46510307" "Concs = 1.529173181"
## [13] "Concs = 1.670981262" "Concs = 1.594325825" "Concs = 1.598291535"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.20234 0.01668
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.56286 -0.15591 0.06192 0.17298 0.32585
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.202336 0.098508 2.054 0.0607 .
## Time[ind] 0.016683 0.001945 8.577 1.03e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2434 on 13 degrees of freedom
## Multiple R-squared: 0.8498, Adjusted R-squared: 0.8383
## F-statistic: 73.57 on 1 and 13 DF, p-value: 1.034e-06
## (Intercept) Time[ind]
## 0.20233603 0.01668311
## 2.5 % 97.5 %
## (Intercept) -0.01047689 0.4151490
## Time[ind] 0.01248113 0.0208851
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.587769932" "Concs = 0.500911907" "Concs = 2.390614252"
## [7] "Concs = 0.732569141" "Concs = 0.819349521" "Concs = 0.882196657"
## [10] "Concs = 1.272480799" "Concs = 1.332879865" "Concs = 1.171215513"
## [13] "Concs = 1.284978616" "Concs = 1.466507839"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.45047 0.01239
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45047 -0.24456 -0.06916 0.04420 1.75424
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.450472 0.232029 1.941 0.0761 .
## Time[ind] 0.012394 0.004981 2.488 0.0285 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5652 on 12 degrees of freedom
## Multiple R-squared: 0.3403, Adjusted R-squared: 0.2853
## F-statistic: 6.19 on 1 and 12 DF, p-value: 0.02854
## (Intercept) Time[ind]
## 0.45047221 0.01239366
## 2.5 % 97.5 %
## (Intercept) -0.055074499 0.9560189
## Time[ind] 0.001540229 0.0232471
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 45" "Indices = 46" "Indices = 47" "Indices = 48"
## [5] "Indices = 49" "Indices = 50" "Indices = 51" "Indices = 52"
## [9] "Indices = 53" "Indices = 54" "Indices = 55" "Indices = 56"
## [13] "Indices = 57" "Indices = 58" "Indices = 59"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.366202494" "Concs = 2.316676352" "Concs = 2.98040696"
## [7] "Concs = 2.746818134" "Concs = 3.431666105" "Concs = 3.294563534"
## [10] "Concs = 3.820882667" "Concs = 4.627112685" "Concs = 4.219456142"
## [13] "Concs = 4.7035697" "Concs = 4.419483485" "Concs = 4.677842802"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 1.16198 0.04474
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.1620 -0.6402 0.2425 0.6568 1.1473
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.161976 0.341679 3.401 0.00474 **
## Time[ind] 0.044744 0.006746 6.632 1.63e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8442 on 13 degrees of freedom
## Multiple R-squared: 0.7719, Adjusted R-squared: 0.7543
## F-statistic: 43.99 on 1 and 13 DF, p-value: 1.632e-05
## (Intercept) Time[ind]
## 1.16197557 0.04474367
## 2.5 % 97.5 %
## (Intercept) 0.42382326 1.90012788
## Time[ind] 0.03016888 0.05931846
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 60" "Indices = 61" "Indices = 62" "Indices = 63"
## [5] "Indices = 64" "Indices = 65" "Indices = 66" "Indices = 67"
## [9] "Indices = 68" "Indices = 69" "Indices = 70" "Indices = 71"
## [13] "Indices = 72" "Indices = 73" "Indices = 74"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.219185884" "Concs = 2.155328801" "Concs = 2.202708256"
## [7] "Concs = 2.811019032" "Concs = 2.229132105" "Concs = 2.319209877"
## [10] "Concs = 3.438186485" "Concs = 3.239731804" "Concs = 3.112249253"
## [13] "Concs = 3.973569475" "Concs = 3.922150065" "Concs = 3.990347195"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.91058 0.03753
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.91058 -0.34028 0.07745 0.48230 0.77459
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.910579 0.255061 3.570 0.00342 **
## Time[ind] 0.037528 0.005036 7.452 4.82e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6302 on 13 degrees of freedom
## Multiple R-squared: 0.8103, Adjusted R-squared: 0.7957
## F-statistic: 55.53 on 1 and 13 DF, p-value: 4.822e-06
## (Intercept) Time[ind]
## 0.91057884 0.03752844
## 2.5 % 97.5 %
## (Intercept) 0.35955278 1.46160490
## Time[ind] 0.02664845 0.04840843
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 75" "Indices = 76" "Indices = 77" "Indices = 78"
## [5] "Indices = 79" "Indices = 80" "Indices = 81" "Indices = 82"
## [9] "Indices = 83" "Indices = 84" "Indices = 85" "Indices = 86"
## [13] "Indices = 87" "Indices = 88" "Indices = 89"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.973173898" "Concs = 4.278761105" "Concs = 5.203600328"
## [7] "Concs = 3.752087918" "Concs = 4.489689601" "Concs = 4.3820044"
## [10] "Concs = 4.18858056" "Concs = 4.787062374" "Concs = 4.819935077"
## [13] "Concs = 5.229225315" "Concs = 5.541134166" "Concs = 5.363637277"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 1.9240 0.0447
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9240 -0.6505 0.1811 0.8021 2.6091
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.92398 0.56293 3.418 0.00458 **
## Time[ind] 0.04470 0.01111 4.022 0.00145 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.391 on 13 degrees of freedom
## Multiple R-squared: 0.5544, Adjusted R-squared: 0.5201
## F-statistic: 16.17 on 1 and 13 DF, p-value: 0.001452
## (Intercept) Time[ind]
## 1.92397917 0.04469949
## 2.5 % 97.5 %
## (Intercept) 0.7078516 3.14010672
## Time[ind] 0.0206871 0.06871189
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 90" "Indices = 91" "Indices = 92" "Indices = 93"
## [5] "Indices = 94" "Indices = 95" "Indices = 96" "Indices = 97"
## [9] "Indices = 98" "Indices = 99" "Indices = 100" "Indices = 101"
## [13] "Indices = 102" "Indices = 103" "Indices = 104"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 3.664975002" "Concs = 5.128116042" "Concs = 3.342678541"
## [7] "Concs = 3.909877303" "Concs = 3.131834777" "Concs = 6.184369077"
## [10] "Concs = 5.034115174" "Concs = 6.997125798" "Concs = 5.513028895"
## [13] "Concs = 5.609126979" "Concs = 6.565737598" "Concs = 6.051117386"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 1.86482 0.05668
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.8648 -1.1362 -0.2317 0.7887 2.6191
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.86482 0.62163 3.000 0.010241 *
## Time[ind] 0.05668 0.01227 4.618 0.000482 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.536 on 13 degrees of freedom
## Multiple R-squared: 0.6213, Adjusted R-squared: 0.5922
## F-statistic: 21.33 on 1 and 13 DF, p-value: 0.0004816
## (Intercept) Time[ind]
## 1.86482214 0.05668337
## 2.5 % 97.5 %
## (Intercept) 0.52186968 3.20777461
## Time[ind] 0.03016682 0.08319991
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 105" "Indices = 106" "Indices = 107" "Indices = 108"
## [5] "Indices = 109" "Indices = 110" "Indices = 111" "Indices = 112"
## [9] "Indices = 113" "Indices = 114" "Indices = 115" "Indices = 116"
## [13] "Indices = 117" "Indices = 118" "Indices = 119"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 4.690841414" "Concs = 4.417155339" "Concs = 6.21277087"
## [7] "Concs = 3.839544319" "Concs = 4.519625245" "Concs = 6.760429619"
## [10] "Concs = 7.2240805" "Concs = 3.468203577" "Concs = 4.462789205"
## [13] "Concs = 8.035064896" "Concs = 8.748204845" "Concs = 7.504701282"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 2.03606 0.06725
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.6030 -1.8222 -0.0537 1.2626 3.1679
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.03606 0.76233 2.671 0.019234 *
## Time[ind] 0.06725 0.01505 4.468 0.000633 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.884 on 13 degrees of freedom
## Multiple R-squared: 0.6056, Adjusted R-squared: 0.5753
## F-statistic: 19.96 on 1 and 13 DF, p-value: 0.0006335
## (Intercept) Time[ind]
## 2.03606128 0.06725212
## 2.5 % 97.5 %
## (Intercept) 0.38913806 3.68298450
## Time[ind] 0.03473369 0.09977056
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 120" "Indices = 121" "Indices = 122" "Indices = 123"
## [5] "Indices = 124" "Indices = 125" "Indices = 126" "Indices = 127"
## [9] "Indices = 128" "Indices = 129" "Indices = 130"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 30"
## [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 17.81066063"
## [4] "Concs = 14.08273374" "Concs = 20.76679639" "Concs = 16.9957259"
## [7] "Concs = 18.08230553" "Concs = 16.51635254" "Concs = 17.9065353"
## [10] "Concs = 19.61630031" "Concs = 17.39520371"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 8.5041 0.1458
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.5041 -3.1238 0.6521 3.7537 7.8875
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.50414 2.90485 2.928 0.0168 *
## Time[ind] 0.14584 0.05633 2.589 0.0293 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.865 on 9 degrees of freedom
## Multiple R-squared: 0.4268, Adjusted R-squared: 0.3632
## F-statistic: 6.702 on 1 and 9 DF, p-value: 0.02927
## (Intercept) Time[ind]
## 8.504137 0.145838
## 2.5 % 97.5 %
## (Intercept) 1.93290585 15.0753686
## Time[ind] 0.01840552 0.2732705
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 0.68 10 2.89 50 75 100 125 150 250
## $ vel: num 2.93 83.42 61.97 223.72 187.64 ...## sub vel
## 1 0.68 2.934844
## 2 10.00 83.415563
## 3 2.89 61.968314
## 4 50.00 223.718355
## 5 75.00 187.642185
## 6 100.00 223.497474
## 7 125.00 283.416841
## 8 150.00 336.260615
## 9 250.00 729.190051
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 1.2697e+04 1.7877e+04 7.1022e-01 0.5005
## e:(Intercept) 4.5773e+03 6.6864e+03 6.8457e-01 0.5156
##
## Residual standard error:
##
## 63.91114 (7 degrees of freedom)
tdlb
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.68"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.159849035" "Concs = 0.171671782" "Concs = 0.137258352"
## [7] "Concs = 0.135498718" "Concs = 0.166579942" "Concs = 0.160555121"
## [10] "Concs = 0.085155894" "Concs = 0.137641779" "Concs = 0.101223849"
## [13] "Concs = 0.041122976" "Concs = 0.056120989" "Concs = 0.040770384"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.0968096 -0.0001003
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.09681 -0.04683 0.01043 0.05570 0.07637
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0968096 0.0272858 3.548 0.00357 **
## Time[ind] -0.0001003 0.0005388 -0.186 0.85514
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06742 on 13 degrees of freedom
## Multiple R-squared: 0.002661, Adjusted R-squared: -0.07406
## F-statistic: 0.03468 on 1 and 13 DF, p-value: 0.8551
## (Intercept) Time[ind]
## 0.0968095889 -0.0001003334
## 2.5 % 97.5 %
## (Intercept) 0.037862112 0.155757066
## Time[ind] -0.001264249 0.001063582
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.540578005" "Concs = 0.535327972" "Concs = 0.549947891"
## [7] "Concs = 0.963906807" "Concs = 0.939249694" "Concs = 0.8832653"
## [10] "Concs = 0.462660817" "Concs = 1.424227752" "Concs = 1.466547242"
## [13] "Concs = 1.470094516" "Concs = 1.424845158" "Concs = 1.471282702"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.23849 0.01462
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.65322 -0.18411 0.07749 0.23407 0.35066
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.238486 0.115619 2.063 0.0597 .
## Time[ind] 0.014623 0.002283 6.406 2.32e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2857 on 13 degrees of freedom
## Multiple R-squared: 0.7594, Adjusted R-squared: 0.7409
## F-statistic: 41.03 on 1 and 13 DF, p-value: 2.323e-05
## (Intercept) Time[ind]
## 0.23848608 0.01462332
## 2.5 % 97.5 %
## (Intercept) -0.011292644 0.48826480
## Time[ind] 0.009691449 0.01955519
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.502687773" "Concs = 0.443748362" "Concs = 1.739413295"
## [7] "Concs = 0.631006803" "Concs = 0.676925019" "Concs = 0.712219102"
## [10] "Concs = 0.887492395" "Concs = 0.922424215" "Concs = 0.774293903"
## [13] "Concs = 0.733501521" "Concs = 0.837366651" "Concs = 0.76078022"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.415973 0.005782
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.41597 -0.18918 -0.00001 0.10515 1.23672
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.415973 0.166466 2.499 0.0266 *
## Time[ind] 0.005782 0.003287 1.759 0.1021
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4113 on 13 degrees of freedom
## Multiple R-squared: 0.1923, Adjusted R-squared: 0.1301
## F-statistic: 3.094 on 1 and 13 DF, p-value: 0.1021
## (Intercept) Time[ind]
## 0.415972672 0.005781657
## 2.5 % 97.5 %
## (Intercept) 0.056345267 0.77560008
## Time[ind] -0.001319173 0.01288249
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59" "Indices = 60"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.598887073" "Concs = 2.355603277" "Concs = 3.141649164"
## [7] "Concs = 3.674320887" "Concs = 4.289723095" "Concs = 4.280136564"
## [10] "Concs = 6.243599629" "Concs = 6.734010485" "Concs = 6.361017452"
## [13] "Concs = 7.195467955" "Concs = 6.834134189" "Concs = 6.9532999"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 1.12601 0.07482
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.1260 -0.9664 0.3036 0.8195 1.1186
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.126011 0.372593 3.022 0.00981 **
## Time[ind] 0.074823 0.007357 10.171 1.48e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9206 on 13 degrees of freedom
## Multiple R-squared: 0.8884, Adjusted R-squared: 0.8798
## F-statistic: 103.4 on 1 and 13 DF, p-value: 1.478e-07
## (Intercept) Time[ind]
## 1.12601129 0.07482339
## 2.5 % 97.5 %
## (Intercept) 0.32107348 1.93094910
## Time[ind] 0.05892992 0.09071685
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 61" "Indices = 62" "Indices = 63" "Indices = 64"
## [5] "Indices = 65" "Indices = 66" "Indices = 67" "Indices = 68"
## [9] "Indices = 69" "Indices = 70" "Indices = 71" "Indices = 72"
## [13] "Indices = 73" "Indices = 74" "Indices = 75"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.526757358" "Concs = 2.313637237" "Concs = 2.49086012"
## [7] "Concs = 3.789628052" "Concs = 3.174642429" "Concs = 3.191438558"
## [10] "Concs = 5.432233942" "Concs = 4.969157891" "Concs = 5.064503301"
## [13] "Concs = 6.712664257" "Concs = 6.597464296" "Concs = 6.484914"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.85930 0.06813
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8593 -0.4502 0.1172 0.4586 0.8863
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.859298 0.247735 3.469 0.00416 **
## Time[ind] 0.068134 0.004892 13.929 3.43e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6121 on 13 degrees of freedom
## Multiple R-squared: 0.9372, Adjusted R-squared: 0.9324
## F-statistic: 194 on 1 and 13 DF, p-value: 3.431e-09
## (Intercept) Time[ind]
## 0.85929819 0.06813407
## 2.5 % 97.5 %
## (Intercept) 0.32409874 1.39449763
## Time[ind] 0.05756657 0.07870156
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 76" "Indices = 77" "Indices = 78" "Indices = 79"
## [5] "Indices = 80" "Indices = 81" "Indices = 82" "Indices = 83"
## [9] "Indices = 84" "Indices = 85" "Indices = 86" "Indices = 87"
## [13] "Indices = 88" "Indices = 89" "Indices = 90"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.987986855" "Concs = 4.62322369" "Concs = 5.738654903"
## [7] "Concs = 5.010985215" "Concs = 6.920302664" "Concs = 6.308852644"
## [10] "Concs = 8.11715413" "Concs = 8.804687457" "Concs = 8.950282552"
## [13] "Concs = 10.81651263" "Concs = 11.45788264" "Concs = 11.01782631"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 1.6755 0.1122
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.6755 -0.8540 -0.2888 0.9047 2.3806
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.67547 0.53930 3.107 0.00834 **
## Time[ind] 0.11217 0.01065 10.534 9.8e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.333 on 13 degrees of freedom
## Multiple R-squared: 0.8951, Adjusted R-squared: 0.8871
## F-statistic: 111 on 1 and 13 DF, p-value: 9.803e-08
## (Intercept) Time[ind]
## 1.675467 0.112175
## 2.5 % 97.5 %
## (Intercept) 0.51037689 2.8405565
## Time[ind] 0.08917031 0.1351796
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 91" "Indices = 92" "Indices = 93" "Indices = 94"
## [5] "Indices = 95" "Indices = 96" "Indices = 97" "Indices = 98"
## [9] "Indices = 99" "Indices = 100" "Indices = 101" "Indices = 102"
## [13] "Indices = 103" "Indices = 104" "Indices = 105"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 4.759629498" "Concs = 6.081131385" "Concs = 4.761075887"
## [7] "Concs = 6.970865526" "Concs = 5.864292522" "Concs = 8.990170569"
## [10] "Concs = 10.29254833" "Concs = 11.89986315" "Concs = 10.55439287"
## [13] "Concs = 12.66145718" "Concs = 13.84087365" "Concs = 12.77355717"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 2.0173 0.1354
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.0173 -1.4830 0.1531 0.8029 2.9118
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.01726 0.65938 3.059 0.00913 **
## Time[ind] 0.13537 0.01302 10.397 1.14e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.629 on 13 degrees of freedom
## Multiple R-squared: 0.8927, Adjusted R-squared: 0.8844
## F-statistic: 108.1 on 1 and 13 DF, p-value: 1.143e-07
## (Intercept) Time[ind]
## 2.0172597 0.1353692
## 2.5 % 97.5 %
## (Intercept) 0.5927540 3.441765
## Time[ind] 0.1072424 0.163496
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 106" "Indices = 107" "Indices = 108" "Indices = 109"
## [5] "Indices = 110" "Indices = 111" "Indices = 112" "Indices = 113"
## [9] "Indices = 114" "Indices = 115" "Indices = 116" "Indices = 117"
## [13] "Indices = 118" "Indices = 119" "Indices = 120"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 6.090475637" "Concs = 5.80525893" "Concs = 8.98551562"
## [7] "Concs = 6.941039356" "Concs = 7.206821805" "Concs = 10.94796175"
## [10] "Concs = 13.80091931" "Concs = 7.457397291" "Concs = 9.668427529"
## [13] "Concs = 16.81467648" "Concs = 18.96446187" "Concs = 16.539466"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 2.1629 0.1654
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6315 -2.1629 -0.1849 1.5790 4.3411
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.16290 1.03599 2.088 0.0571 .
## Time[ind] 0.16543 0.02046 8.087 1.98e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.56 on 13 degrees of freedom
## Multiple R-squared: 0.8342, Adjusted R-squared: 0.8214
## F-statistic: 65.41 on 1 and 13 DF, p-value: 1.985e-06
## (Intercept) Time[ind]
## 2.1628981 0.1654341
## 2.5 % 97.5 %
## (Intercept) -0.07522754 4.4010238
## Time[ind] 0.12124239 0.2096258
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 121" "Indices = 122" "Indices = 123" "Indices = 124"
## [5] "Indices = 125" "Indices = 126" "Indices = 127" "Indices = 128"
## [9] "Indices = 129" "Indices = 130" "Indices = 131"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 30"
## [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 22.19280552"
## [4] "Concs = 17.62020275" "Concs = 24.15778887" "Concs = 20.49970666"
## [7] "Concs = 25.33183553" "Concs = 23.63873667" "Concs = 25.85088774"
## [10] "Concs = 28.34728168" "Concs = 25.77673742"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 9.7157 0.2368
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.716 -3.962 1.410 4.017 8.926
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.71573 3.28235 2.96 0.01596 *
## Time[ind] 0.23676 0.06365 3.72 0.00477 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.628 on 9 degrees of freedom
## Multiple R-squared: 0.6059, Adjusted R-squared: 0.5621
## F-statistic: 13.84 on 1 and 9 DF, p-value: 0.004774
## (Intercept) Time[ind]
## 9.715734 0.236762
## 2.5 % 97.5 %
## (Intercept) 2.29053916 17.140929
## Time[ind] 0.09276905 0.380755
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 0.68 10 2.89 50 75 100 125 150 250
## $ vel: num -0.502 73.117 28.908 374.117 340.67 ...## sub vel
## 1 0.68 -0.5016668
## 2 10.00 73.1166041
## 3 2.89 28.9082836
## 4 50.00 374.1169252
## 5 75.00 340.6703300
## 6 100.00 560.8747995
## 7 125.00 676.8458299
## 8 150.00 827.1705102
## 9 250.00 1183.8100663
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 4725.9044 1685.0376 2.8046 0.0263
## e:(Intercept) 742.9043 326.0030 2.2788 0.0567
##
## Residual standard error:
##
## 47.48388 (7 degrees of freedom)
fipronil
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 10" "Concs = 10" "Concs = 10"
## [4] "Concs = 7.601993848" "Concs = 11.87171779" "Concs = 8.347482218"
## [7] "Concs = 12.54233702" "Concs = 9.213313367" "Concs = 10.38856477"
## [10] "Concs = 12.36949156" "Concs = 8.215365646" "Concs = 11.17931895"
## [13] "Concs = 12.71923746" "Concs = 9.99477721"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 9.71360 0.01483
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.3880 -1.0265 0.2087 1.3248 2.3838
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.71360 0.69685 13.939 8.96e-09 ***
## Time[ind] 0.01483 0.01333 1.112 0.288
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.635 on 12 degrees of freedom
## Multiple R-squared: 0.09348, Adjusted R-squared: 0.01794
## F-statistic: 1.237 on 1 and 12 DF, p-value: 0.2878
## (Intercept) Time[ind]
## 9.7136033 0.0148301
## 2.5 % 97.5 %
## (Intercept) 8.1953041 11.23190240
## Time[ind] -0.0142172 0.04387739
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 15" "Indices = 16" "Indices = 17" "Indices = 18"
## [5] "Indices = 19" "Indices = 20" "Indices = 21" "Indices = 22"
## [9] "Indices = 23" "Indices = 24" "Indices = 25" "Indices = 26"
## [13] "Indices = 27" "Indices = 28" "Indices = 29"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 2.89" "Concs = 2.89" "Concs = 2.89"
## [4] "Concs = 0.961731316" "Concs = 0.608701865" "Concs = 2.021395291"
## [7] "Concs = 0.34095865" "Concs = 1.416552854" "Concs = 4.678731136"
## [10] "Concs = 1.597568113" "Concs = 2.059112975" "Concs = 4.336224939"
## [13] "Concs = 0.73593197" "Concs = 1.01143428" "Concs = 2.098949857"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 2.330304 -0.007551
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7628 -0.8010 -0.1956 0.5597 2.5749
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.330304 0.537794 4.333 0.000812 ***
## Time[ind] -0.007551 0.010619 -0.711 0.489590
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.329 on 13 degrees of freedom
## Multiple R-squared: 0.03744, Adjusted R-squared: -0.0366
## F-statistic: 0.5057 on 1 and 13 DF, p-value: 0.4896
## (Intercept) Time[ind]
## 2.330304214 -0.007550889
## 2.5 % 97.5 %
## (Intercept) 1.16847156 3.49213686
## Time[ind] -0.03049123 0.01538945
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 30" "Indices = 31" "Indices = 32" "Indices = 33"
## [5] "Indices = 34" "Indices = 35" "Indices = 36" "Indices = 37"
## [9] "Indices = 38" "Indices = 39" "Indices = 40" "Indices = 41"
## [13] "Indices = 42" "Indices = 43" "Indices = 44"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 50" "Concs = 50" "Concs = 50"
## [4] "Concs = 223.3849191" "Concs = 19.09530124" "Concs = 61.85004879"
## [7] "Concs = 76.72890033" "Concs = 65.4447593" "Concs = 59.88633813"
## [10] "Concs = 74.09066447" "Concs = 65.54242812" "Concs = 39.55208359"
## [13] "Concs = 66.15498564" "Concs = 23.55175796" "Concs = 58.25965938"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 74.6926 -0.2339
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -52.088 -24.693 -7.788 6.970 152.201
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 74.6926 19.3363 3.863 0.00196 **
## Time[ind] -0.2339 0.3818 -0.613 0.55064
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 47.78 on 13 degrees of freedom
## Multiple R-squared: 0.02807, Adjusted R-squared: -0.0467
## F-statistic: 0.3754 on 1 and 13 DF, p-value: 0.5506
## (Intercept) Time[ind]
## 74.6925954 -0.2339266
## 2.5 % 97.5 %
## (Intercept) 32.919023 116.466168
## Time[ind] -1.058744 0.590891
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 45" "Indices = 46" "Indices = 47" "Indices = 48"
## [5] "Indices = 49" "Indices = 50" "Indices = 51" "Indices = 52"
## [9] "Indices = 53" "Indices = 54" "Indices = 55" "Indices = 56"
## [13] "Indices = 57" "Indices = 58"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 75" "Concs = 75" "Concs = 75"
## [4] "Concs = 35.05455395" "Concs = 40.30349338" "Concs = 44.1381674"
## [7] "Concs = 38.08049817" "Concs = 38.34527612" "Concs = 89.31881211"
## [10] "Concs = 40.27279664" "Concs = 55.95173867" "Concs = 37.82415225"
## [13] "Concs = 32.32010713" "Concs = 45.93427684"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 61.7586 -0.2706
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.64 -14.86 -2.33 12.54 35.68
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 61.7586 6.9259 8.917 1.22e-06 ***
## Time[ind] -0.2706 0.1388 -1.950 0.0749 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17.1 on 12 degrees of freedom
## Multiple R-squared: 0.2407, Adjusted R-squared: 0.1774
## F-statistic: 3.803 on 1 and 12 DF, p-value: 0.0749
## (Intercept) Time[ind]
## 61.7586076 -0.2706222
## 2.5 % 97.5 %
## (Intercept) 46.6682795 76.84893559
## Time[ind] -0.5729691 0.03172479
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 59" "Indices = 60" "Indices = 61" "Indices = 62"
## [5] "Indices = 63" "Indices = 64" "Indices = 65" "Indices = 66"
## [9] "Indices = 67" "Indices = 68" "Indices = 69" "Indices = 70"
## [13] "Indices = 71" "Indices = 72" "Indices = 73"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 100" "Concs = 100" "Concs = 100"
## [4] "Concs = 65.75118371" "Concs = 61.03836189" "Concs = 86.42270417"
## [7] "Concs = 18.77293974" "Concs = 84.04356305" "Concs = 89.30314297"
## [10] "Concs = 60.95565287" "Concs = 89.79580177" "Concs = 90.59062961"
## [13] "Concs = 56.03613412" "Concs = 94.58659729" "Concs = 89.70085579"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 82.175 -0.078
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -61.062 -15.897 9.468 16.185 19.431
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 82.1752 9.3919 8.750 8.28e-07 ***
## Time[ind] -0.0780 0.1854 -0.421 0.681
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.21 on 13 degrees of freedom
## Multiple R-squared: 0.01343, Adjusted R-squared: -0.06246
## F-statistic: 0.1769 on 1 and 13 DF, p-value: 0.6809
## (Intercept) Time[ind]
## 82.17518132 -0.07800026
## 2.5 % 97.5 %
## (Intercept) 61.8852665 102.4650961
## Time[ind] -0.4786239 0.3226233
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 74" "Indices = 75" "Indices = 76" "Indices = 77"
## [5] "Indices = 78" "Indices = 79" "Indices = 80" "Indices = 81"
## [9] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [13] "Indices = 86" "Indices = 87" "Indices = 88"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 125" "Concs = 125" "Concs = 125"
## [4] "Concs = 62.24891641" "Concs = 54.68420677" "Concs = 91.10795719"
## [7] "Concs = 51.66702524" "Concs = 65.6950903" "Concs = 112.1237445"
## [10] "Concs = 62.81350539" "Concs = 74.14828799" "Concs = 93.87631612"
## [13] "Concs = 59.80299767" "Concs = 82.33654045" "Concs = 89.20514072"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 97.5253 -0.3217
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -38.016 -18.796 -1.593 22.439 27.475
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 97.5253 10.1778 9.582 2.95e-07 ***
## Time[ind] -0.3217 0.2010 -1.601 0.133
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.15 on 13 degrees of freedom
## Multiple R-squared: 0.1646, Adjusted R-squared: 0.1004
## F-statistic: 2.562 on 1 and 13 DF, p-value: 0.1335
## (Intercept) Time[ind]
## 97.525349 -0.321659
## 2.5 % 97.5 %
## (Intercept) 75.5374944 119.5132038
## Time[ind] -0.7558084 0.1124904
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 89" "Indices = 90" "Indices = 91" "Indices = 92"
## [5] "Indices = 93" "Indices = 94" "Indices = 95" "Indices = 96"
## [9] "Indices = 97" "Indices = 98" "Indices = 99" "Indices = 100"
## [13] "Indices = 101" "Indices = 102" "Indices = 103"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 150" "Concs = 150" "Concs = 150"
## [4] "Concs = 37.15191594" "Concs = 76.95257401" "Concs = 82.83018255"
## [7] "Concs = 89.28298886" "Concs = 103.9076465" "Concs = 88.89209516"
## [10] "Concs = 75.20034761" "Concs = 99.21349783" "Concs = 86.10641447"
## [13] "Concs = 85.35534061" "Concs = 86.89358929" "Concs = 19.45762438"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 115.9094 -0.6109
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -69.593 -16.302 6.326 25.199 34.091
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 115.9094 13.0063 8.912 6.73e-07 ***
## Time[ind] -0.6109 0.2568 -2.379 0.0334 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 32.14 on 13 degrees of freedom
## Multiple R-squared: 0.3033, Adjusted R-squared: 0.2497
## F-statistic: 5.659 on 1 and 13 DF, p-value: 0.03337
## (Intercept) Time[ind]
## 115.9093503 -0.6109334
## 2.5 % 97.5 %
## (Intercept) 87.810974 144.00772609
## Time[ind] -1.165735 -0.05613202
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 104" "Indices = 105" "Indices = 106" "Indices = 107"
## [5] "Indices = 108" "Indices = 109" "Indices = 110" "Indices = 111"
## [9] "Indices = 112" "Indices = 113" "Indices = 114" "Indices = 115"
## [13] "Indices = 116" "Indices = 117" "Indices = 118"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 200" "Concs = 200" "Concs = 200"
## [4] "Concs = 143.5820327" "Concs = 117.0381728" "Concs = 105.3992543"
## [7] "Concs = 120.601107" "Concs = 115.1379412" "Concs = 126.1830373"
## [10] "Concs = 91.91948648" "Concs = 106.6462813" "Concs = 72.50149496"
## [13] "Concs = 112.4063583" "Concs = 105.3992543" "Concs = 111.7531537"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 160.8018 -0.8264
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.006 -20.084 -4.823 25.656 39.198
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 160.8018 12.1956 13.185 6.7e-09 ***
## Time[ind] -0.8264 0.2408 -3.432 0.00446 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 30.13 on 13 degrees of freedom
## Multiple R-squared: 0.4754, Adjusted R-squared: 0.435
## F-statistic: 11.78 on 1 and 13 DF, p-value: 0.00446
## (Intercept) Time[ind]
## 160.8018480 -0.8264276
## 2.5 % 97.5 %
## (Intercept) 134.454923 187.1487728
## Time[ind] -1.346647 -0.3062086
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 119" "Indices = 120" "Indices = 121" "Indices = 122"
## [5] "Indices = 123" "Indices = 124" "Indices = 125" "Indices = 126"
## [9] "Indices = 127" "Indices = 128" "Indices = 129" "Indices = 130"
## [13] "Indices = 131" "Indices = 132" "Indices = 133"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 250" "Concs = 250" "Concs = 250"
## [4] "Concs = 105.2844752" "Concs = 83.9166222" "Concs = 57.25407999"
## [7] "Concs = 71.31021926" "Concs = 93.93871253" "Concs = 36.95777127"
## [10] "Concs = 77.4873567" "Concs = 101.3134582" "Concs = 91.54349597"
## [13] "Concs = 58.38865626" "Concs = 74.14665992" "Concs = 61.1620649"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 164.214 -1.368
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -86.434 -45.128 9.433 26.595 85.786
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 164.2141 24.5533 6.688 1.5e-05 ***
## Time[ind] -1.3684 0.4848 -2.823 0.0144 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 60.67 on 13 degrees of freedom
## Multiple R-squared: 0.38, Adjusted R-squared: 0.3323
## F-statistic: 7.967 on 1 and 13 DF, p-value: 0.01439
## (Intercept) Time[ind]
## 164.21412 -1.36839
## 2.5 % 97.5 %
## (Intercept) 111.170007 217.2582237
## Time[ind] -2.415744 -0.3210361
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 10 2.89 50 75 100 125 150 200 250
## $ vel: num 74.2 -37.8 -1169.6 -1353.1 -390 ...## sub vel
## 1 10.00 74.15048
## 2 2.89 -37.75444
## 3 50.00 -1169.63320
## 4 75.00 -1353.11079
## 5 100.00 -390.00131
## 6 125.00 -1608.29494
## 7 150.00 -3054.66698
## 8 200.00 -4132.13800
## 9 250.00 -6841.95007
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) -1.4458e+06 4.7941e+05 -3.0158e+00 0.0195
## e:(Intercept) 6.7499e+04 2.3731e+04 2.8443e+00 0.0249
##
## Residual standard error:
##
## 975.4389 (7 degrees of freedom)
fipsulf
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.226052779" "Concs = 0.249546426" "Concs = 0.249495111"
## [7] "Concs = 0.556306401" "Concs = 0.629523416" "Concs = 0.545734442"
## [10] "Concs = 1.029532274" "Concs = 1.020828782" "Concs = 1.121529265"
## [13] "Concs = 1.478049545" "Concs = 1.552223152" "Concs = 1.605171177"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.01178 0.01724
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08563 -0.02090 -0.01178 0.02194 0.10045
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0117752 0.0194862 0.604 0.556
## Time[ind] 0.0172434 0.0003848 44.817 1.23e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04815 on 13 degrees of freedom
## Multiple R-squared: 0.9936, Adjusted R-squared: 0.9931
## F-statistic: 2009 on 1 and 13 DF, p-value: 1.235e-15
## (Intercept) Time[ind]
## 0.01177521 0.01724336
## 2.5 % 97.5 %
## (Intercept) -0.03032210 0.05387251
## Time[ind] 0.01641215 0.01807457
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0" "Concs = 0"
## [7] "Concs = 0.072417652" "Concs = 0.105189206" "Concs = 0.093830232"
## [10] "Concs = 0.446059868" "Concs = 0.501873862" "Concs = 1.937676963"
## [13] "Concs = 0.541481009" "Concs = 0.713021528" "Concs = 0.948269563"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## -0.06729 0.01089
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37110 -0.15983 -0.09602 0.05149 1.35172
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.067286 0.164967 -0.408 0.6900
## Time[ind] 0.010887 0.003257 3.342 0.0053 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4076 on 13 degrees of freedom
## Multiple R-squared: 0.4622, Adjusted R-squared: 0.4208
## F-statistic: 11.17 on 1 and 13 DF, p-value: 0.005297
## (Intercept) Time[ind]
## -0.06728624 0.01088737
## 2.5 % 97.5 %
## (Intercept) -0.423675199 0.28910272
## Time[ind] 0.003850487 0.01792426
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.509901494" "Concs = 0.497072024" "Concs = 0.573048602"
## [7] "Concs = 0.208702278" "Concs = 1.224307072" "Concs = 0.86186791"
## [10] "Concs = 2.640613398" "Concs = 2.278728642" "Concs = 1.938091721"
## [13] "Concs = 3.288556396" "Concs = 2.79424236" "Concs = 2.85277407"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.21639 0.03149
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.9524 -0.2164 -0.1917 0.1181 1.8212
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.216386 0.251326 0.861 0.405
## Time[ind] 0.031491 0.004962 6.346 2.55e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.621 on 13 degrees of freedom
## Multiple R-squared: 0.756, Adjusted R-squared: 0.7372
## F-statistic: 40.27 on 1 and 13 DF, p-value: 2.552e-05
## (Intercept) Time[ind]
## 0.2163859 0.0314908
## 2.5 % 97.5 %
## (Intercept) -0.32657121 0.75934309
## Time[ind] 0.02077013 0.04221147
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.61596018" "Concs = 0.004496637" "Concs = 0.393574273"
## [7] "Concs = 1.00896852" "Concs = 1.080335369" "Concs = 1.122428808"
## [10] "Concs = 0.794034486" "Concs = 1.567175192" "Concs = 1.445091993"
## [13] "Concs = 1.567376573" "Concs = 1.397216044"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.19848 0.01565
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4288 -0.1985 -0.1010 0.3013 0.4543
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.19848 0.12829 1.547 0.148
## Time[ind] 0.01565 0.00257 6.090 5.42e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3168 on 12 degrees of freedom
## Multiple R-squared: 0.7555, Adjusted R-squared: 0.7351
## F-statistic: 37.08 on 1 and 12 DF, p-value: 5.421e-05
## (Intercept) Time[ind]
## 0.19848307 0.01565313
## 2.5 % 97.5 %
## (Intercept) -0.08104254 0.47800868
## Time[ind] 0.01005261 0.02125366
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 60" "Indices = 61" "Indices = 62" "Indices = 63"
## [5] "Indices = 64" "Indices = 65" "Indices = 66" "Indices = 67"
## [9] "Indices = 68" "Indices = 69" "Indices = 70" "Indices = 71"
## [13] "Indices = 72" "Indices = 73" "Indices = 74"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 1.037370756" "Concs = 1.004548869" "Concs = 1.211451943"
## [7] "Concs = 1.770038982" "Concs = 1.964421756" "Concs = 2.082784287"
## [10] "Concs = 2.421230649" "Concs = 2.716290502" "Concs = 2.511880669"
## [13] "Concs = 2.884476336" "Concs = 3.658963096" "Concs = 3.101044324"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.45746 0.03334
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.57339 -0.40714 0.05415 0.25624 0.62519
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.457459 0.159292 2.872 0.0131 *
## Time[ind] 0.033338 0.003145 10.600 9.12e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3936 on 13 degrees of freedom
## Multiple R-squared: 0.8963, Adjusted R-squared: 0.8883
## F-statistic: 112.4 on 1 and 13 DF, p-value: 9.118e-08
## (Intercept) Time[ind]
## 0.4574592 0.0333378
## 2.5 % 97.5 %
## (Intercept) 0.11333032 0.80158804
## Time[ind] 0.02654299 0.04013261
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 75" "Indices = 76" "Indices = 77" "Indices = 78"
## [5] "Indices = 79" "Indices = 80" "Indices = 81" "Indices = 82"
## [9] "Indices = 83" "Indices = 84" "Indices = 85" "Indices = 86"
## [13] "Indices = 87" "Indices = 88" "Indices = 89"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 1.0685532" "Concs = 1.193964217" "Concs = 1.061157254"
## [7] "Concs = 1.739690158" "Concs = 1.568026457" "Concs = 1.831902381"
## [10] "Concs = 2.58185903" "Concs = 2.518118409" "Concs = 2.706182414"
## [13] "Concs = 3.388713261" "Concs = 3.265199632" "Concs = 3.360717697"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.38590 0.03504
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.38590 -0.22611 0.09385 0.18765 0.39495
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.385901 0.113655 3.395 0.00478 **
## Time[ind] 0.035035 0.002244 15.612 8.42e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2808 on 13 degrees of freedom
## Multiple R-squared: 0.9494, Adjusted R-squared: 0.9455
## F-statistic: 243.7 on 1 and 13 DF, p-value: 8.42e-10
## (Intercept) Time[ind]
## 0.38590066 0.03503517
## 2.5 % 97.5 %
## (Intercept) 0.14036476 0.63143656
## Time[ind] 0.03018707 0.03988327
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 90" "Indices = 91" "Indices = 92" "Indices = 93"
## [5] "Indices = 94" "Indices = 95" "Indices = 96" "Indices = 97"
## [9] "Indices = 98" "Indices = 99" "Indices = 100" "Indices = 101"
## [13] "Indices = 102" "Indices = 103" "Indices = 104"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 1.513101462" "Concs = 1.254618226" "Concs = 1.316915121"
## [7] "Concs = 1.847166036" "Concs = 2.06265471" "Concs = 2.225655093"
## [10] "Concs = 3.029089226" "Concs = 2.818619179" "Concs = 2.892261352"
## [13] "Concs = 3.395108251" "Concs = 3.493680617" "Concs = 3.346621743"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.57092 0.03527
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5709 -0.3742 0.1547 0.2802 0.5967
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.570919 0.171417 3.331 0.00542 **
## Time[ind] 0.035268 0.003385 10.420 1.11e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4236 on 13 degrees of freedom
## Multiple R-squared: 0.8931, Adjusted R-squared: 0.8848
## F-statistic: 108.6 on 1 and 13 DF, p-value: 1.114e-07
## (Intercept) Time[ind]
## 0.57091928 0.03526787
## 2.5 % 97.5 %
## (Intercept) 0.20059443 0.94124413
## Time[ind] 0.02795582 0.04257992
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 105" "Indices = 106" "Indices = 107" "Indices = 108"
## [5] "Indices = 109" "Indices = 110" "Indices = 111" "Indices = 112"
## [9] "Indices = 113" "Indices = 114" "Indices = 115" "Indices = 116"
## [13] "Indices = 117" "Indices = 118" "Indices = 119"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.921840151" "Concs = 1.265455207" "Concs = 0.083794693"
## [7] "Concs = 1.758009212" "Concs = 1.131761977" "Concs = 2.14032494"
## [10] "Concs = 3.119569212" "Concs = 5.219960219" "Concs = 3.68483357"
## [13] "Concs = 4.382618411" "Concs = 4.121095689" "Concs = 4.42249183"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.12797 0.05185
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8219 -0.3919 -0.1280 0.2171 1.9810
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.12797 0.28111 0.455 0.656
## Time[ind] 0.05185 0.00555 9.342 3.94e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6946 on 13 degrees of freedom
## Multiple R-squared: 0.8703, Adjusted R-squared: 0.8604
## F-statistic: 87.26 on 1 and 13 DF, p-value: 3.942e-07
## (Intercept) Time[ind]
## 0.12796676 0.05185001
## 2.5 % 97.5 %
## (Intercept) -0.47932924 0.73526276
## Time[ind] 0.03985897 0.06384104
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 120" "Indices = 121" "Indices = 122" "Indices = 123"
## [5] "Indices = 124" "Indices = 125" "Indices = 126" "Indices = 127"
## [9] "Indices = 128" "Indices = 129" "Indices = 130" "Indices = 131"
## [13] "Indices = 132" "Indices = 133" "Indices = 134"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.688691412" "Concs = 0.680203691" "Concs = 0.671715969"
## [7] "Concs = 1.128032043" "Concs = 1.057705208" "Concs = 1.0791266"
## [10] "Concs = 1.670842039" "Concs = 1.655483305" "Concs = 1.672054571"
## [13] "Concs = 2.11584115" "Concs = 2.394723427" "Concs = 2.276703681"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.2111 0.0238
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.23753 -0.14388 0.03278 0.11632 0.20285
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.211083 0.063521 3.323 0.0055 **
## Time[ind] 0.023803 0.001254 18.978 7.35e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.157 on 13 degrees of freedom
## Multiple R-squared: 0.9652, Adjusted R-squared: 0.9625
## F-statistic: 360.2 on 1 and 13 DF, p-value: 7.353e-11
## (Intercept) Time[ind]
## 0.21108314 0.02380321
## 2.5 % 97.5 %
## (Intercept) 0.07385384 0.34831244
## Time[ind] 0.02109362 0.02651279
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 10 2.89 50 75 100 125 150 200 250
## $ vel: num 86.2 54.4 157.5 78.3 166.7 ...## sub vel
## 1 10.00 86.21679
## 2 2.89 54.43687
## 3 50.00 157.45399
## 4 75.00 78.26567
## 5 100.00 166.68901
## 6 125.00 175.17585
## 7 150.00 176.33933
## 8 200.00 259.25003
## 9 250.00 119.01603
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 179.92190 32.01471 5.61997 0.0008
## e:(Intercept) 11.21512 13.83476 0.81065 0.4443
##
## Residual standard error:
##
## 49.9681 (7 degrees of freedom)
exposure experiment analysis
Results presentation and discussion for parent analytes (atrazine, triadimenon, and fipronil) and their xenobiotic metabolites.
Toxicity of parents and metabolites discussion.
Microsomal analysis of soil and amphibian data for 0 (soil only), 2, 4, 12, 24, and 48 hours after exposure.
Database has factors for time, parent (mapped to analyte), analyte (can be either parent or metabolite), matrix (amphibian or soil), and tank (potentially a nuisance variable).
## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame': 352 obs. of 6 variables:
## $ time : int 2 2 2 2 4 4 4 4 12 12 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 3.07 3.69 4.7 1.89 7.62 ...
## $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 4 1 2 3 4 1 2 ...
## - attr(*, "vars")=List of 4
## ..$ : symbol parent
## ..$ : symbol analyte
## ..$ : symbol matrix
## ..$ : symbol time
## - attr(*, "drop")= logi TRUE
## - attr(*, "indices")=List of 86
## ..$ : int 0 1 2 3
## ..$ : int 4 5 6 7
## ..$ : int 8 9 10 11
## ..$ : int 12 13 14 15
## ..$ : int 16 17 18 19
## ..$ : int 20 21 22 23
## ..$ : int 24 25 26 27
## ..$ : int 28 29 30 31
## ..$ : int 32 33 34 35
## ..$ : int 36 37 38 39
## ..$ : int 40 41 42 43
## ..$ : int 88 89 90 91
## ..$ : int 92 93 94 95
## ..$ : int 96 97 98 99
## ..$ : int 100 101 102 103
## ..$ : int 104 105 106 107
## ..$ : int 108 109 110 111
## ..$ : int 112 113 114 115
## ..$ : int 116 117 118 119
## ..$ : int 120 121 122 123
## ..$ : int 124 125 126 127
## ..$ : int 128 129 130 131
## ..$ : int 44 45 46 47
## ..$ : int 48 49 50 51
## ..$ : int 52 53 54 55
## ..$ : int 56 57 58 59
## ..$ : int 60 61 62 63
## ..$ : int 64 65 66 67
## ..$ : int 68 69 70 71
## ..$ : int 72 73 74 75
## ..$ : int 76 77 78 79
## ..$ : int 80 81 82 83
## ..$ : int 84 85 86 87
## ..$ : int 264 265 266 267
## ..$ : int 268 269 270 271
## ..$ : int 272 273 274 275
## ..$ : int 276 277 278 279
## ..$ : int 280 281 282 283
## ..$ : int 284 285 286 287 288 289 290 291
## ..$ : int 292 293 294 295
## ..$ : int 296 297 298 299
## ..$ : int 300 301 302 303
## ..$ : int 304 305 306 307
## ..$ : int 308 309 310 311
## ..$ : int 312 313 314 315
## ..$ : int 316 317 318 319
## ..$ : int 320 321 322 323
## ..$ : int 324 325 326 327
## ..$ : int 328 329 330 331 332 333 334 335
## ..$ : int 336 337 338 339
## ..$ : int 340 341 342 343
## ..$ : int 344 345 346 347
## ..$ : int 348 349 350 351
## ..$ : int 176 177 178 179
## ..$ : int 180 181 182 183
## ..$ : int 184 185 186 187
## ..$ : int 188 189 190 191
## ..$ : int 192 193 194 195
## ..$ : int 196 197 198 199
## ..$ : int 200 201 202 203
## ..$ : int 204 205 206 207
## ..$ : int 208 209 210 211
## ..$ : int 212 213 214 215
## ..$ : int 216 217 218 219
## ..$ : int 220 221 222 223
## ..$ : int 224 225 226 227
## ..$ : int 228 229 230 231
## ..$ : int 232 233 234 235
## ..$ : int 236 237 238 239
## ..$ : int 240 241 242 243
## ..$ : int 244 245 246 247
## ..$ : int 248 249 250 251
## ..$ : int 252 253 254 255
## ..$ : int 256 257 258 259
## ..$ : int 260 261 262 263
## ..$ : int 132 133 134 135
## ..$ : int 136 137 138 139
## ..$ : int 140 141 142 143
## ..$ : int 144 145 146 147
## ..$ : int 148 149 150 151
## ..$ : int 152 153 154 155
## ..$ : int 156 157 158 159
## ..$ : int 160 161 162 163
## ..$ : int 164 165 166 167
## ..$ : int 168 169 170 171
## ..$ : int 172 173 174 175
## - attr(*, "group_sizes")= int 4 4 4 4 4 4 4 4 4 4 ...
## - attr(*, "biggest_group_size")= int 8
## - attr(*, "labels")='data.frame': 86 obs. of 4 variables:
## ..$ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## ..$ analyte: Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## ..$ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
## ..$ time : int 2 4 12 24 48 0 2 4 12 24 ...
## ..- attr(*, "vars")=List of 4
## .. ..$ : symbol parent
## .. ..$ : symbol analyte
## .. ..$ : symbol matrix
## .. ..$ : symbol time
## ..- attr(*, "drop")= logi TRUE## Source: local data frame [352 x 6]
## Groups: parent, analyte, matrix, time [86]
##
## time parent analyte matrix conc replicate
## (int) (fctr) (fctr) (fctr) (dbl) (fctr)
## 1 2 atrazine atrazine amphib 3.068203 1
## 2 2 atrazine atrazine amphib 3.689640 2
## 3 2 atrazine atrazine amphib 4.701166 3
## 4 2 atrazine atrazine amphib 1.892494 4
## 5 4 atrazine atrazine amphib 7.624610 1
## 6 4 atrazine atrazine amphib 4.134300 2
## 7 4 atrazine atrazine amphib 2.050779 3
## 8 4 atrazine atrazine amphib 7.626486 4
## 9 12 atrazine atrazine amphib 2.452278 1
## 10 12 atrazine atrazine amphib 3.786893 2
## .. ... ... ... ... ... ...## Source: local data frame [86 x 7]
## Groups: parent, analyte, matrix [?]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine amphib 2 4 3.337876 1.1753225
## 2 atrazine atrazine amphib 4 4 5.359044 2.7518903
## 3 atrazine atrazine amphib 12 4 3.123811 1.2566289
## 4 atrazine atrazine amphib 24 4 1.554919 0.6096102
## 5 atrazine atrazine amphib 48 4 1.001887 0.3545473
## 6 atrazine atrazine soil 0 4 15.930920 2.5911041
## 7 atrazine atrazine soil 2 4 19.029034 4.3534303
## 8 atrazine atrazine soil 4 4 18.770091 2.6953158
## 9 atrazine atrazine soil 12 4 20.614190 3.8918511
## 10 atrazine atrazine soil 24 4 24.996196 4.4473828
## .. ... ... ... ... ... ... ...## <!-- html table generated in R 3.2.3 by xtable 1.8-2 package -->
## <!-- Thu Feb 11 19:05:42 2016 -->
## <table border=1>
## <tr> <th> </th> <th> parent </th> <th> analyte </th> <th> matrix </th> <th> time </th> <th> count </th> <th> ConcMean </th> <th> ConcSD </th> </tr>
## <tr> <td align="right"> 1 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 3.34 </td> <td align="right"> 1.18 </td> </tr>
## <tr> <td align="right"> 2 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 5.36 </td> <td align="right"> 2.75 </td> </tr>
## <tr> <td align="right"> 3 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 3.12 </td> <td align="right"> 1.26 </td> </tr>
## <tr> <td align="right"> 4 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 1.55 </td> <td align="right"> 0.61 </td> </tr>
## <tr> <td align="right"> 5 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 1.00 </td> <td align="right"> 0.35 </td> </tr>
## <tr> <td align="right"> 6 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 15.93 </td> <td align="right"> 2.59 </td> </tr>
## <tr> <td align="right"> 7 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 19.03 </td> <td align="right"> 4.35 </td> </tr>
## <tr> <td align="right"> 8 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 18.77 </td> <td align="right"> 2.70 </td> </tr>
## <tr> <td align="right"> 9 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 20.61 </td> <td align="right"> 3.89 </td> </tr>
## <tr> <td align="right"> 10 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 25.00 </td> <td align="right"> 4.45 </td> </tr>
## <tr> <td align="right"> 11 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 26.43 </td> <td align="right"> 4.38 </td> </tr>
## <tr> <td align="right"> 12 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 13 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
## <tr> <td align="right"> 14 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.05 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 15 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 16 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 17 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 18 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 19 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 20 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 21 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 22 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 23 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.33 </td> <td align="right"> 0.12 </td> </tr>
## <tr> <td align="right"> 24 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.94 </td> <td align="right"> 0.76 </td> </tr>
## <tr> <td align="right"> 25 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 1.08 </td> <td align="right"> 0.51 </td> </tr>
## <tr> <td align="right"> 26 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 1.99 </td> <td align="right"> 1.35 </td> </tr>
## <tr> <td align="right"> 27 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.66 </td> <td align="right"> 0.53 </td> </tr>
## <tr> <td align="right"> 28 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 29 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> -0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 30 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 31 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.07 </td> </tr>
## <tr> <td align="right"> 32 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
## <tr> <td align="right"> 33 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.06 </td> </tr>
## <tr> <td align="right"> 34 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 1.87 </td> <td align="right"> 1.35 </td> </tr>
## <tr> <td align="right"> 35 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 1.30 </td> <td align="right"> 0.52 </td> </tr>
## <tr> <td align="right"> 36 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.57 </td> <td align="right"> 0.24 </td> </tr>
## <tr> <td align="right"> 37 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.27 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 38 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.21 </td> <td align="right"> 0.13 </td> </tr>
## <tr> <td align="right"> 39 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 8 </td> <td align="right"> 0.41 </td> <td align="right"> 0.45 </td> </tr>
## <tr> <td align="right"> 40 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.24 </td> </tr>
## <tr> <td align="right"> 41 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.82 </td> <td align="right"> 0.17 </td> </tr>
## <tr> <td align="right"> 42 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.70 </td> <td align="right"> 0.11 </td> </tr>
## <tr> <td align="right"> 43 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.36 </td> <td align="right"> 0.06 </td> </tr>
## <tr> <td align="right"> 44 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.35 </td> <td align="right"> 0.29 </td> </tr>
## <tr> <td align="right"> 45 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.40 </td> <td align="right"> 0.48 </td> </tr>
## <tr> <td align="right"> 46 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.61 </td> <td align="right"> 0.57 </td> </tr>
## <tr> <td align="right"> 47 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 1.25 </td> <td align="right"> 0.53 </td> </tr>
## <tr> <td align="right"> 48 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.91 </td> <td align="right"> 0.57 </td> </tr>
## <tr> <td align="right"> 49 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 8 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 50 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 51 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 52 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 53 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 54 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 55 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 56 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 57 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 58 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 59 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 60 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 61 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 62 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 63 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 64 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 65 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 66 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.13 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 67 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 68 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 69 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.03 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 70 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 71 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 72 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 73 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 74 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 75 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 76 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.39 </td> <td align="right"> 0.08 </td> </tr>
## <tr> <td align="right"> 77 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.55 </td> <td align="right"> 0.30 </td> </tr>
## <tr> <td align="right"> 78 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.75 </td> <td align="right"> 0.32 </td> </tr>
## <tr> <td align="right"> 79 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.86 </td> </tr>
## <tr> <td align="right"> 80 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.25 </td> <td align="right"> 0.08 </td> </tr>
## <tr> <td align="right"> 81 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 3.11 </td> <td align="right"> 0.85 </td> </tr>
## <tr> <td align="right"> 82 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 3.66 </td> <td align="right"> 1.34 </td> </tr>
## <tr> <td align="right"> 83 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 5.28 </td> <td align="right"> 0.37 </td> </tr>
## <tr> <td align="right"> 84 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 5.93 </td> <td align="right"> 1.00 </td> </tr>
## <tr> <td align="right"> 85 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 4.82 </td> <td align="right"> 0.32 </td> </tr>
## <tr> <td align="right"> 86 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 4.18 </td> <td align="right"> 0.44 </td> </tr>
## </table>The amphibian data set summary statistics. Atrazine peaks at 4 hours and then declines monotonically. DEA peaks at 12 hours and DIA at 24. Fipronil steadily declines from its first observation at 2 hours with fipronil sulfone not peaking until 24 hours. Triadimenon peaks at 24 hours with its metabolites tdla and tdlb peaking at 4 hours.
## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame': 86 obs. of 7 variables:
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
## $ time : int 2 4 12 24 48 0 2 4 12 24 ...
## $ count : int 4 4 4 4 4 4 4 4 4 4 ...
## $ ConcMean: num 3.34 5.36 3.12 1.55 1 ...
## $ ConcSD : num 1.175 2.752 1.257 0.61 0.355 ...
## - attr(*, "vars")=List of 3
## ..$ : symbol parent
## ..$ : symbol analyte
## ..$ : symbol matrix
## - attr(*, "drop")= logi TRUE## Source: local data frame [6 x 7]
## Groups: parent, analyte, matrix [2]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine amphib 2 4 3.33787563 1.17532253
## 2 atrazine atrazine amphib 4 4 5.35904387 2.75189034
## 3 atrazine atrazine amphib 12 4 3.12381130 1.25662887
## 4 atrazine atrazine amphib 24 4 1.55491895 0.60961016
## 5 atrazine atrazine amphib 48 4 1.00188749 0.35454734
## 6 atrazine dea amphib 2 4 0.01389877 0.00522407## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine amphib 2 4 3.33787563 1.17532253
## 2 atrazine atrazine amphib 4 4 5.35904387 2.75189034
## 3 atrazine atrazine amphib 12 4 3.12381130 1.25662887
## 4 atrazine atrazine amphib 24 4 1.55491895 0.60961016
## 5 atrazine atrazine amphib 48 4 1.00188749 0.35454734
## 6 atrazine dea amphib 2 4 0.01389877 0.00522407
## 7 atrazine dea amphib 4 4 0.04436711 0.02843181
## 8 atrazine dea amphib 12 4 0.05402182 0.01282235
## 9 atrazine dea amphib 24 4 0.03652473 0.01310278
## 10 atrazine dea amphib 48 4 0.01951501 0.01958540
## 11 atrazine dia amphib 2 4 0.32878185 0.12495746
## 12 atrazine dia amphib 4 4 0.94192818 0.76074427
## 13 atrazine dia amphib 12 4 1.08350960 0.50576827
## 14 atrazine dia amphib 24 4 1.98835970 1.34925248
## 15 atrazine dia amphib 48 4 0.66238821 0.53051448## [1] "atrazine"
## [1] "dea"
## [1] "dia"## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 fipronil fipronil amphib 2 4 1.8670398 1.34631230
## 2 fipronil fipronil amphib 4 4 1.3005836 0.52188454
## 3 fipronil fipronil amphib 12 4 0.5659565 0.24026633
## 4 fipronil fipronil amphib 24 4 0.2676732 0.05106111
## 5 fipronil fipronil amphib 48 4 0.2119504 0.13140536
## 6 fipronil fipsulf amphib 2 4 0.3465734 0.28711156
## 7 fipronil fipsulf amphib 4 4 0.3966089 0.47739157
## 8 fipronil fipsulf amphib 12 4 0.6129114 0.57346517
## 9 fipronil fipsulf amphib 24 4 1.2528179 0.52648677
## 10 fipronil fipsulf amphib 48 4 0.9067126 0.56596417## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
##
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
## (int), count (int), ConcMean (dbl), ConcSD (dbl)The soil data set summary statistics. Atrazine in soil showing an upwards trend (need to test if significant) with dia and dea levels very low indicating little degradation in soil over the 48 hour period. Fipronil and triadimenon data also indicating little degradation in soil.
## Source: local data frame [18 x 7]
## Groups: parent, analyte, matrix [3]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine soil 0 4 15.930919692 2.591104068
## 2 atrazine atrazine soil 2 4 19.029034412 4.353430337
## 3 atrazine atrazine soil 4 4 18.770091080 2.695315758
## 4 atrazine atrazine soil 12 4 20.614190363 3.891851074
## 5 atrazine atrazine soil 24 4 24.996195532 4.447382801
## 6 atrazine atrazine soil 48 4 26.434744900 4.377099498
## 7 atrazine dea soil 0 4 0.000000000 0.000000000
## 8 atrazine dea soil 2 4 0.001570429 0.000633009
## 9 atrazine dea soil 4 4 0.002999216 0.001537652
## 10 atrazine dea soil 12 4 0.005469015 0.004234880
## 11 atrazine dea soil 24 4 0.007308439 0.001736211
## 12 atrazine dea soil 48 4 0.008784632 0.003772339
## 13 atrazine dia soil 0 4 0.000000000 0.000000000
## 14 atrazine dia soil 2 4 -0.007727286 0.007374085
## 15 atrazine dia soil 4 4 0.020538600 0.020166308
## 16 atrazine dia soil 12 4 0.077036921 0.067772652
## 17 atrazine dia soil 24 4 0.042975804 0.030007793
## 18 atrazine dia soil 48 4 0.063693292 0.058241606## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 fipronil fipronil soil 2 8 0.40768123 0.447265792
## 2 fipronil fipronil soil 4 4 0.86826316 0.244191727
## 3 fipronil fipronil soil 12 4 0.81738069 0.169691335
## 4 fipronil fipronil soil 24 4 0.70225877 0.108745058
## 5 fipronil fipronil soil 48 4 0.35560948 0.058543752
## 6 fipronil fipsulf soil 2 8 0.01022479 0.012898421
## 7 fipronil fipsulf soil 4 4 0.02193831 0.010765665
## 8 fipronil fipsulf soil 12 4 0.01829893 0.005013814
## 9 fipronil fipsulf soil 24 4 0.01917848 0.009139211
## 10 fipronil fipsulf soil 48 4 0.01262887 0.005517408## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
##
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
## (int), count (int), ConcMean (dbl), ConcSD (dbl)pdf(paste(micro.graphics,"data_mean_scatterplot",".pdf", sep=""))
par(mfrow=c(3,1))
print(parents)## [1] atrazine triadimefon fipronil
## Levels: atrazine fipronil triadimefon for(parent in parents){
i=0
print(parent)
temp.parent <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
print(temp.parent)
parent.analytes <- unique(temp.parent$analyte)
for(analyte in parent.analytes){
print(parent)
print(analyte)
analytetemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$analyte==analyte),]
xvalues <- as.numeric(as.character(analytetemp$time))
points.y <- micro.amphib[which(micro.amphib$analyte==analyte),]$conc
points.x <- as.numeric(as.character(micro.amphib[which(micro.amphib$analyte==analyte),]$time))
#create empty plot if needed
if(i==0){
parenttemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
maxconc <- max(points.y)
plot(xvalues,analytetemp$ConcMean,type="l", xlim=c(0,48),
ylim = c(0,maxconc), main=parent,col="black", xlab="Hours", ylab="Concentration")
axis(1,at=xvalues)
i=1
}
#add line for parent metabolite
if(analyte %in% parents){
lines(xvalues,analytetemp$ConcMean,type="l",col="red")
points(points.x, points.y, col = "red")
}else{
#add line for daughter metabolite
lines(xvalues,analytetemp$ConcMean,type="l",col="blue")
points(points.x, points.y, col = "blue")
}
}
}## [1] "atrazine"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine amphib 2 4 3.33787563 1.17532253
## 2 atrazine atrazine amphib 4 4 5.35904387 2.75189034
## 3 atrazine atrazine amphib 12 4 3.12381130 1.25662887
## 4 atrazine atrazine amphib 24 4 1.55491895 0.60961016
## 5 atrazine atrazine amphib 48 4 1.00188749 0.35454734
## 6 atrazine dea amphib 2 4 0.01389877 0.00522407
## 7 atrazine dea amphib 4 4 0.04436711 0.02843181
## 8 atrazine dea amphib 12 4 0.05402182 0.01282235
## 9 atrazine dea amphib 24 4 0.03652473 0.01310278
## 10 atrazine dea amphib 48 4 0.01951501 0.01958540
## 11 atrazine dia amphib 2 4 0.32878185 0.12495746
## 12 atrazine dia amphib 4 4 0.94192818 0.76074427
## 13 atrazine dia amphib 12 4 1.08350960 0.50576827
## 14 atrazine dia amphib 24 4 1.98835970 1.34925248
## 15 atrazine dia amphib 48 4 0.66238821 0.53051448
## [1] "atrazine"
## [1] "atrazine"## [1] "atrazine"
## [1] "dea"
## [1] "atrazine"
## [1] "dia"
## [1] "triadimefon"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 triadimefon tdla amphib 2 4 0.05514470 0.021089764
## 2 triadimefon tdla amphib 4 4 0.08150175 0.046221502
## 3 triadimefon tdla amphib 12 4 0.03632384 0.015222899
## 4 triadimefon tdla amphib 24 4 0.02400790 0.007522554
## 5 triadimefon tdla amphib 48 4 0.01549908 0.004845715
## 6 triadimefon tdlb amphib 2 4 0.08362714 0.016364595
## 7 triadimefon tdlb amphib 4 4 0.13009543 0.054315693
## 8 triadimefon tdlb amphib 12 4 0.07664673 0.048553355
## 9 triadimefon tdlb amphib 24 4 0.04183235 0.011652266
## 10 triadimefon tdlb amphib 48 4 0.02950214 0.003438978
## 11 triadimefon triadimefon amphib 2 4 0.38678831 0.075852995
## 12 triadimefon triadimefon amphib 4 4 0.54862458 0.300394386
## 13 triadimefon triadimefon amphib 12 4 0.75491439 0.318237965
## 14 triadimefon triadimefon amphib 24 4 0.86540039 0.860421208
## 15 triadimefon triadimefon amphib 48 4 0.24868748 0.079848623
## [1] "triadimefon"
## [1] "tdla"## [1] "triadimefon"
## [1] "tdlb"
## [1] "triadimefon"
## [1] "triadimefon"
## [1] "fipronil"
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 fipronil fipronil amphib 2 4 1.8670398 1.34631230
## 2 fipronil fipronil amphib 4 4 1.3005836 0.52188454
## 3 fipronil fipronil amphib 12 4 0.5659565 0.24026633
## 4 fipronil fipronil amphib 24 4 0.2676732 0.05106111
## 5 fipronil fipronil amphib 48 4 0.2119504 0.13140536
## 6 fipronil fipsulf amphib 2 4 0.3465734 0.28711156
## 7 fipronil fipsulf amphib 4 4 0.3966089 0.47739157
## 8 fipronil fipsulf amphib 12 4 0.6129114 0.57346517
## 9 fipronil fipsulf amphib 24 4 1.2528179 0.52648677
## 10 fipronil fipsulf amphib 48 4 0.9067126 0.56596417
## [1] "fipronil"
## [1] "fipronil"## [1] "fipronil"
## [1] "fipsulf"dev.off()## quartz_off_screen
## 2la de da
turn times series to zoo objects
estimate lambdas using maximum likelihood for each time series
library(maxLik)
MLexp <- function(times, data){
expLik <- function(param) { y <- data t <- times alpha1 <- param[1] lambda1 <- param[2]-1(alpha1-lambda1t) - y/(exp(alpha1-lambda1*t)) }
max.fit <- maxLik(expLik, start = c(1,1)) crit <- qt(.975, length(data)-2) max.intercept.CI <- c(summary(max.fit)\(est[1,1]-crit*summary(max.fit)\)est[1,2],summary(max.fit)\(est[1,1]+crit*summary(max.fit)\)est[1,2]) max.decayrate.CI <- c(-1summary(max.fit)\(est[2,1]-crit*summary(max.fit)\)est[2,2],-1summary(max.fit)\(est[2,1]+crit*summary(max.fit)\)est[2,2]) max.halflife.CI <- c(log(2)/max.decayrate.CI[2],log(2)/max.decayrate.CI[1])
paste(“MLE for Initial Concentration =”,max.fit\(est[1], "MLE for decay rate =", max.fit\)est[2], “MLE for half life =”, -log(.5)/max.fit$est[2])
temp.list <- list(max.fit\(est[1], max.fit\)est[2], -log(.5)/max.fit$est[2], max.intercept.CI, max.decayrate.CI, max.halflife.CI, vcov(max.fit) ) return(temp.list) }
MLexp.intercept <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[1]] }
MLexp.decayrate <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[2]] }
MLexp.halflife <- function(times,data) { temp.fit <- MLexp(times,data) temp.fit[[3]] }
MLexp.intercept.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[4]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }
MLexp.decayrate.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[5]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }
MLexp.halflife.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[6]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }
microsome experiment analysis
data in csv format